Page 1
t+€ ist-ts anJ dj s+qYr€g ,
No.,, Fve.",
AAe'c &
Z'D & ba^ce
o4"
I-f-c4F
+
of el e v'rhfu.
"F "0.a&E" = .{,
ob .Lalae,
g:6o",
-- ? = ,+c.
LJ.tLt- * ? 5ft1: Bc.
-n€,h0.b-
k Fcrlce ., Pof" F oF otre'wat&n ,.o4 {oof "|,
,ht-ocoe v :- >Om. =BC
ele,vaP,a.., ob top o$ to.,x,"
"b f*r.- H: ir ': {q
oh*..hD.tr fi"h"alz.
= a{Beht-sl4{-oporiiz jpd._
16-',6 = opforiD r,b164g+E tt* tiae,(eO
i.e tangd = ''+g)-o
)-o ro-^6dP.
-zoxG
aoJ3
'foto n H*sr oh : 2O"D .n.
, )9 -6"1( 2o'','
- 6oo=€,
--i ti.,r. r ",
k F,,."'ce-, (rrtr
.le..6tt
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Page 2
rll\loLt tL.,o.,-,
{** a"qte- t-%"6fe-4et^
@e = tdt'.!rl riJg-Atfl,tz^utr..
Cosgb': Bc"+c.
I - z)p
,+L
"4c > -z;q.l, s'
. &o6$ eb
=)
+
e-'n [[
r^ra!l
= l.l r-.r
J,aAAe- .X,
6.
b& t-^'c-.
r/r8tc
|*,Au,t
hJo- trnU
l1-n-
l. LJntl = zm a BOLeFwtno {oob o}- la&...nade td .[ad&v ..,l+6
e 5 6cre '
+ r.ratt 4= 1 = :48.
a ttora\f()ABL (".-
ffrar.d
a-dteA -l-rfc."Alt
.t-aa 6e' : -46Bc.
'.13 = ite,1,
-'. +.',e.6C'f o[ 'eall rr- 2{3.O.
foos = opporilT ridg4Jjaccat rr%a,
9. -a{{::-Ecn.
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Page 3
+,k8?e"h oh
4\te made
,Itr
b{
e
"j
H : tor) :Ag
u,f+6 grou.d ( +c';zo"tot)
Jel-
tF *.&"-{**
Jr.e
noog+t,
.re F\.r
r € ri b-
"F <r(]Ltr.re
a- '-'ft+t
atova dafa ,8,
.tEt., rof
,f"rqcr",q le -48C.(l
*c
I
A
=) sfc' 4S" = ,+g*c'
lo tn.t,
roJi-.L!J."{e U-[e-6tr,
"h = I oJi.n.
t*'i1-0-
5.#urn\J
-fl€'%hl o{ kiF +o.-a/5,,.lSo.hu- olt x l,"i"tu(
9-
J-e^q+t, ol sf'f^q -tqli(
6-*oct-,d = +5rr: Ag
*?+t Ar.-,aV
6o"
=9 =*U
\poLa.e.r<.
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Page 4
,f LLi(
j*'-+5.- c
$e ".
fqFr
rit;
oI
st.o = oPporth, efda'
J.'61ote otue-'
3r^ bO :
.{.
:f.SX r_
v3
5o"[ -o,Lf,f,g .X
V
3 3 x50{3
= SoG m.
V H'..,?.
o-tove dala,
t2' 3-..."t .ta
-49_+t'
€=
-L --
fl_
ot-v
6.
t"fc.re., p"fllkilf -- qo ..o.
tfl o*'h .., ft{., q.rd ri s.!5&
t'^"1 /!q)L8l.1-e.h!'t- eh .[Ec, kglu'
L^
o:r,al p Aa
d-fr*..*".'a.oq le
48r,,'--"'1..-"'i
I
I
.[a"Cfi.
A-6te-
9r
Jf,
.l-e-g+t oh ,*.?
"ootd e
i c-e =
cdL Y eP{e(?.t- .tr-a
,tL,ot -, .tFe., tf
Ye f€t?^f trEe, atlare ' da Fa.
{,"a- .' " o I tloo TR 0..
r io L.t o.'9{ a .1 l' 'oo ^glE -4et '
qU
("'* #66r
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Page 5
*o."o = opporil' r-ide
'fujo.. €^F {fd..,
11B(.
9H -oItJ., a4e,L , \ Wn^A-'^ TFo"-"o
lc--6-
EL
qo- = &-.li-))*- r-r>,\lE,/
loa: lgrrrltg+;:-l5r'
H'lQLr'rs>) = lDlx rsLt-trt6+r rrS) = (1e119:-
HL r p6x15.;r-281
H'--. f.loxr(-\rL i+- ,/
H = goxr_E_lJ._ _ r r.1t
o[ kilz fvom 6-o0]"d
louu
,$o.g 4&.Bc
n =*t.fl.ro.
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Page 6
? 6lve.
ve ih"c_cr[ l-ct 'rr, .&
Dftt-a''ce \etsu:te..
4"g'. o[ n tcvah'o',
Aorv-n6*.1.; t.d #"A o*bfIa''c' a"d ot!."rro" = lo.cr. 3 gC
,fr fog Joco.r "t = 44.ofu
"b
WL
&'tJ^
''t1*t
f,arp = scPt..
-+ Jor 60"
+ $++o
? {--
a:
+4u "t ele"of,"- of {96[a6,rt--ffi p = eoe
.tre,!l''t "l- fy"fr = Jr. - Ao
"ht2c.r "f to..*.r = 4. : AB.
^.esY.( e ^i- nlt aLovt Acnta'
d,2-"" 'fq?' fr (". "-r
,?", +-,"""nler 4 lt€c r,4cBD.
hl-,e", e ,i *At.- {'io.'eL
Yr"A [.F Lia
*o- < = 496C
2 fo-" 1So= t-t
+o.
+ ha +oxJ
= *o.
H -- ao.o,
Lnqo .t6ar
. 3lillq =+o
= +o[G)
+ot.Ri)+o Lr
.+s!--r)
5t"j'l.-o.
{_t-t-4o'
-- +Dx O?A!
-. . 4,: Sr.>t"r-;
't"'n-,!xr o[ iour"-- qo- -Leiql-,r ofi frn.*6n =s-l.:+.n.
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Page 7
+c?ht- ,t
J-e-F r.r &l{ L!.r€ it ir LnoLen ol poP.fc.
urrt+r-"
,Aef6ht-
6'o"e'' TEah *tl" 'na.le t.d koLe" gr 'r
ft\-oe-d e = 6d.
WL
*.a-u"
tra'
* o. ?
y ar,.zt {o 6aLe o pof.F c. - 4-, . = ec .
Ats = Ac+Bc
? H= Ae-f i+ +c=G=+E,o.
referc^t AF-. <tLo'r. dcttso- P^ IEL ("( ""'Jkr l+ fi."-^r {o.'r a.6k.r *<\a^6f c -*at
6fi6d = BcC&
'ld = +,, H .lr.
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Page 8
Glts-b1 = 1"tEJa- hG = 2h
(:+€)t, = rsQ.
.1.., = tsrE x2*J-3
>_:J^3
a*GI a.rf"-.' t ff i^+ dz ,.,o..,! te."
I n.m"r.t 4.,"$ g.,.r.. "fiotrt,ir olct,=) I = Es2l-g,
2:-{f,)-
= rEt>J.3_g
}l = tst2r3..3)
{"ei1nt 4 LsoLen poP" f -6"- fr.ror.r,'a
: rs l>r.r -s)"n
'Le'"qu'r o[ .rqz *t"g.t-.61 t,,- 5-. = A+.
A-Vte "F el",..t-i-, ,F *, "h dq"o66 = 6a.--q.
+d" .h eLvoF,t, oi totro $ fl{_j-=""=U.Let +e,6tl- ofi -16-"- te 11 -,r.: uAB- '
t fi LL't ' vc?\ tlc^t .1tr? aLoue do la Pnyq-}4td"* ", <,h-,. rGe^ i, d*- l-.'^.€t( ,/ i , ^ . ,ceb P, cot.%r, -ABc & i4 cl"Jed- U" ,/ fi t"f*li.1,ts:.18. / ,,."'Lt.*"-
4Jfcrc€^h
I 649 =
Hm
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Page 9
fa" q = Bou
I ta''6o" = 4an oo
-F= 48BC
-fat 3e" - *BC
\rs (3rG=Bc.
fr_t5 -oBC
tte e- -- +'r/ect ;Gt
3. -- r-i -rE- + 8Ft = H+f
**t,oq 6t-q
9l Fve.'-q
H
'Fl =S e u=C: I'(..n.
il -toltz". H = 9.rcn.t]
f ohe.vcrbt"o-, (A)
c,-:alkeJ 5o.', {*o.,
o( = 3oo -
{-1rr poP"f 6; +o
.48 = 5o.n.
e tc vrrF,%o **"o'r ,4e.ond gof.F e * F= t€'
+nAte of ntzvobloo of t.T .b -b,'t"" J=o.
$*rF
Le t-
3oF"t
.+z
-tk;
"h4^€k
No,,, leF Lrr v3vtle.rt 36-
6Pre^ cJccta P. (*'- "il dqa.
rt .{o..".rr +""^7t- 'tCs '"rfti-'
J.,"".'otl. BcE l'' fl- t z:c'--6'
L e t 4p Po l^'t "l +d"' ' 12qlu
Hm = cD'gL = /' '('t:, '
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Page 10
I * '---:!un .€& n-"^^Alo s ,1 A&, *d.:Fn"o = o>eoltF ,rPd e-++----
-4al icr ce " FrfJe
JRo
*ct ot = CuAL.
AstBc.
\3 5ot)L+ 5ottr: HJi *O
fi\ p.O -, qo+ H\: .E
-lcrr\F = C'D
Bc,
=r *.' ^ r--" ^ lt.-.-""_-...-)'
+ {1-_ H.;
)C = H -/.i_=- \'/{3
- uc.
-----.rt
! *re ,/
+ n= >_Q.[ = z9{:
llc iqt 'r o\ to-"' I I - e g[ roQ'
l1le f .!Fe n,T* ,h ,t4,,.1o,., "b Lor.z.v
url^p," A"?Xe 4 e Lvah{., &lo.ao9 Un. ;r ..D:sc-- q I
.tlco occoxJF.l *o Y""Lle*'
Jeogtx rh ,TFe aLaJc{.r c',ftr, :a-gle of e le "a
(p=+*l ir lto+ic).n. = Bb.
t.c.ii
ro,
!
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Page 11
fTUJE0
*"'a"*J-',"a"dc
5"t-
Yefett4t
.IFe-, tt
-4+c u
,I1|e, qAovc Aata f;
{*.-! o- i,,^LVI- +Bo
f-.-l"t"l,u?H. zg--1$.
{--
p
Jtr,c
fon*. aG-BL
? *o"uo" = t-t
+ x= u _d)\l3
r\.&ukh"trr 6 r:- H-to-(/'n
H -ro : !_"la
O
.i3t-ro.r: = H
!3-DH E- 106
+ l-l : lo,l:rl5r
H: loJS x lEtt _
@-u[cr9I bJe tJ:a tD
5 !_3 t{]J> a3'666
{ Rrrt,"".vrt.t. clc.,qn ry,atb"
I '"h"^"t48-'? d*.h, 'f-
L"t* ,1 a-.1^u
+lefqar o[ fo"xv= 23.46.n_
I,e,t +*hF efi- *e'*" Le +r'n - -4G
".6e"t a^€t.
"'tf. & e
f,cr.,6r = opporili] atde,
-,$a-1trc eal c 8de_.
+-fa^([c
.ttsao
fft.a = 4e.E;7 fon 45. - rt
' f,+lD
+ 5ctro 1H:) x,: H *ro -6
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Page 12
lL.LeF
Jpt-
Lu Sa pa-vacl. sLt1; aF Afghert- pofnF *,c t D L4 Pofb hrf,".l.) aye I Do.r) o.
1vrv.t-
tpl.'e te- *.o.,,ehvahLr f"o..
.[Fio CD: tDo.o.
*r-' fl"yoc.d
:of p"ta-c1"uf--
rtg = q-.
;:a%r u*t.e#o jc.rb-
oLr c w<.t'.f,rr' ,1'o,fnb = r.D.*furt a',Ar,- *'"o,-BL o.,c- o'[- .t5o
cr6te
ef(attr
fl.od+')ar€ f
D&Fa.,t<.
para cf'r-tF
Rc(1ra(f
ffiftc{..dd
porP"ts C = 4S o, f,.J
4Tle ob- el'a-vc-ho-' {-o- f,,,,?,
r o = eo". tF]
Lel- * t? .t6e po,flh _1irrr vrrhtall 1- Joc.,,, ,6-&
pvo.ch.rtr-
l_er ur d....,-dFL:,Ta* *"^d ''A-." a{ A^or-n r. L'A&h
-*ed ir +-L"(1. a,'l -A€D ,,",rl.rdeJ F^ pr
-\er *'f*.U.t. roorlu J ef .
Mor r9^.-..- .9..21.6
fl1 {o-",r .6a
L,., f+r-,
e""+ 18,I oori DF->z- <---{
r-t------------ '/*a're = opporiF r?lp Ij --+e_l
/ +4"<rc"4c rflde_.|r__ _____,-__l
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Page 13
LLOrr"( = ,48c8
ta''4So= l-tI OO+2(,
I Do+r, E- H- ..---O
lf*t,h eb- .tou.,c,
l"r ,+'4 g' t.
*a.,o -tr- 4eDe"
*an6o"
H=-
ta.
€*.
o&o./Er_ = roo tx,(.la-g o. = 1oc,
t = l9o-^ €*l€-t Cr.. = loo( _fri_r)
L
9 :c = toL€tt).,,,_\ v 5 .- /_, ^ - ".tu U.
.rAz+ D
+ )r = Foc!..la)-)I t- = ,36.6.r_D. ri O
H = .I8xr3t.6 = r.ig? xt36.6 = 236.6"r).
_O
fro.,.7 grouJU
fi = 2J6.6 .D.
pavaco'ut {6'tttrt: 136.6"co
-nxto.''s- aefgc,,f o$- 3a'.acAuf
Pftha'ca LeF-ce., poF.t tDhr.e.
ffr*t L jLLr F ot te...rolrtro P.r
h : Ar3 : tsb .n.
ti',o oliz c h (r) Jhc 6rouoJ.
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Page 14
*.nre of dca-erePo-, f, obir.t n' farnxJ = p= r,so. = z*Ate.
-+-6rz- o[ &g<,crfm ofi oL(ecr- n * [+xllrre]
LX h&' -- at : bD "_ LABTB
faxl\'a'e]lrF A'gr=x gtg..,t
Ai Lpe ,e prur.t ,Il,t o to,,J J-t"!% q|"'0.,". , XF.. ?r- & ar rl,6.,,a
vril:r. z-.g=ao' A'l':' reJtstt-----+{<_--.1
t.n -t \./ac'ts "-Bu +-!a'-dt, 3$ one- + lf-r?.ctu,-dal t^d. & o .e;
'L Ar, -
* fo.ad
O P"@ )
+
ttd = 'lg -nG
tans = AeArg
ta-1s"= r5oot(
Lr t =- rso .-@
= l5o- gDl r x2^,,' ")
= 63 + o")
*re\ = 6=..1 rD.
hgBe'
: lSD
!+ ISO _ rSO€
a+ 5!_l3 . rsovi
'/ :L = lso _. 5913
= lso_ 86.6
ba[r:ee,, otlec hDlrFo,'r .
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Page 15
*n2V "h
Le t- a)e,
e-Lvat ro,:- of tog
-J*ct-. go,9,t- A., at =
advontpA S.ou2t-,
-ttseo 4g = tso.l.,
o[- ]o..rr.r 4.o.,,3d.
.4 +{, s b.d t5D.o
CDAD
h"F=
t an r,o"
H:
cD,BD
_tl
,l{5 =2 J =
lEo+a,
: r-J J3. '-(l)
l5O + r+ ^ Lr.a" ->,,/-i,
u /g1\ - rsot,rz )
aef6rr
fi,/:
e
h.
{G-r r(zltso x rj3
= l5o.
: 45G = 45xt +22r>9.1-o
of, -+orue- = lz? q.'o.
+"Aln- efi efcva.LJu-, o$ +"p of, ,lo,,.re" {wo.r r,ecr:ol
poi.t g, € = eo..
Lel tt-e.fr;r ef -l-ot _rz, ctr = t-l .D.
Xt u)e- wep-ere.l J1=<, oto,," d..1a
f" {"..- 'h d,A:"" -tq". fc {u,.-.
43A-". dr ,rlo..-r r.:ftr z>=1d. ##;H5r$- ro. 'f€D,r o^€leJ -l..Pa1,le , ooe otr P.dvlee o,fl<,ft e JEe,.,
to-< =
t^r,;lo"
t5o+:{-
f"O.-o
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Page 16
Dr1to,rc- beFus"n..,
Le l- a',e 36\t rb
b h t orce 6e t-.-.r"..,
"f Lt'e Yeff"'tlenF
t'V*"" , ''[Fe'' frr.or" tl z-t' =Jo"-
g. *iyr"r il"a- L . fF, F. cl
'..1eJoh -e__'Jheo
fc.r < :
fo.-, :o">Df 1-
zo"1- 1 - +lC -D
(, ." (_1, => 2of It€
Lr.,Da- toJ-3 _-E--la%* olguDlrlo,,r" ol
0
of a0z,,a.l-.15 "b
A ,'4,-fot-.rc"
ac creJ
JEZ
do'--d
+"p f toLoe' {-o- pef^y-6d -- zo".
-f.p ,h toco". -J"o_ 3ol_ Fe
F-ao"1+8 = !b.r.co = 't'-qpo8r g {-o.., (oof o}
ctLn"e, da\a, f- uf.
t!tr* o! tlot -yt
$tt
4nA14
of e)+vaffse
J.
:GD
€p&D
-J^
'l"fa'7|- ,oX "n-
4" &o
fa^o - r^ED
*a^ad ^ -l-r
:--.
:c = | -
/i\./],
. c1
=hG ]-tG-!) = '.o.,tz I= ?9€ 'toxJ3 =
->o =) 4 l*'3r.o.
lo..r1l
*ot:.. 4 = i+S)ro,
toi,:r' -(-.o.' pP.'t O = po.r-16; - 36".,.
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Page 17
let 4sJn e fg t-,t-
E. J5o bc,fld .%.1
o$ lAo hrrb,?ln
eLc.,.rffo", "$ 1c3
hr"ftdi'-? 4:soo.
eLe-vatf6-' 4 +Df
t,'L?td.ot F= 60:
od cp Lz, .t92
{ lb-. :-h = *B
ofi to.,-:e" -f..- -irp "b-
F_> r tt *--{
BD = bx = t)c' .r, . ,48 = XD = ..1-r : rs'.D.
5ir{ g ,lq-e.
"rfghF -l-.-fa,-61s h Dio "f nt,!.drd;.d a,2!.
*ctn < = CxAX
? 144 3c)" : alic.
o6
AG.-O;c
.t :cG = a+iS.
*ngte o[
Aoalt o].4V
D ir lo.rz 6eti,,:eu. *orue^ x Lcdtd.%? tsb : >L .
l-et he,.tXtrts of lt>t'te* aLove b,n6,pn- L",A.,',3f b)( vzg- <rc,,t d.r)e- aL-.at". J,ztsa- Fn
+'.- oD {h*. rrtsea fr {o.-.-r{ f6*'" nr al.ouro. r'fr.- z-a -6'4 olro d..ano 4y Il bD ) zAKc- :1f .
.ge,e 46DX lt a *ecFc.,111L
of +o,,,"' t*- t"t6-- "6_
A
B
*cr.r A : Cor- E;? -1a,. kf -- o_r 15-
&
T
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Page 18
0f i5:
? &o-=
+L=rt!:l = -+') 'n
loq-26t alova
bet ttee n tor.,sc "
: .J. S.x l.+B L= 12'11 -t.
6rot-o,J - .A r-o,
= lqt+.S _ '2>.S"o.
arJ t..ftdf-q = t>.9e ^n(]
+,ogt t
dt Fo.,ce
IB
,f
Le t- 48 fz .tbz tfou-,zv c-,d Bd te d{.?lr-6pOo JIEZ to*.,.
D&t-o..,c" oi Ff"F o[ ok-vafr%o*o,,re " $1>= 1-o--hl" eh e tr-vab-.eo efr +-p oi-A-,gte of e[evaF,% + t"HG- 4
Jet- '6ei3hF o[ -fat sc" =12y, :: t":l.
'heftht o[ ;ole = (3, : eg.
Jfiz obu" d.,io fu veyete.frel ,P.
tlJ ^l.or'ro
t'i*{r LA -- 1o"
J-*- +'-F or-
{b- ob dt-""
-f- t.-,
rooc ludel
ta"s --4{jacznt-rlde'
*hht -+-&.€le
fl"6rt-$ft4a: eo".
{r"6 ga" teJ p = acr-
o,r6le &o,01e
JhA.
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Page 19
*ana = 4c'qt
-Fo', Lo' =
)cru =
u=(
:Li l{q
1J6.
9J3-sG
fonp = 1!1AD
fa"' eo' = :cI
r= ? = ,=.]3
'li= 5 1L.o.
t_-1JL
5t194
16'.9'
= 6J3 = 6x t.+3 L: l o.3q z .D,
-haf6ht of fouoe"
-be.!r,t eb- Fle t'5-1.1 a^1b.33).rr,
Let- f.?ffat{X I*e<, Ae,'gr"t ba *e,L4 LtJ o,r!u-n ed ;tha h J6e, *ree & L'-epn ab-
pofrl c-*d" -...oa[a bd bookeo go..l- cB, t,.'+r-,
?"roudr"s Jo' = g'
D fr bq.,ce bett,eeo $ooi o$ -L*e. 1o gof,.r .rhc"e lffor.r ch e,r
E".ou.t gt* = S- ,
O"rflto ofr *"ee = +" = *c+esr. -- Ac+Lg.
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IE, a-bove
(PX.'e eL
t {o---ntPoo,{l'otrrr.
..e3'<re''t ''" ,fbL -J".- "b
llgr''t + tvez _
CoS 3o" =
48 be
-Fo',66or cAABI
-!- = c+.v3B
cA= g
!3
eBltc4: tt r IV3 ..J3
= 8G-
G=
cei =
4gcd
_8-c6t
t6E
:3=8x5GE
LaF
{^gta
AB = 4e3lr o1-
+l.rq.te- eh e bwolftro
Jhe :bocoer cird
e l+vcthoon *f t"f
taweo
"h
Bo ba JR" $\rtogyot- l'!du.oT d'c.- p
a=af,> I D"...
i;oy o[ dta.?rrd$F +-D- p
P= +4,I e t- Ae %C.r
o '|lapfaf $- =BD = (a, .v,..
Tbe ^L-tz ,P., {o--,,ah.o- & we,p-er.<oFzJ
'o" 1o-' of {,fo^" ^ tLtot'L:x'>'
bilA LA =7o".
G a -fghu o.gted 'l-ta"3.le'
ft o^e- + fre. 'Bchded'
bFt.drt"ll-
lt^ *)B
asgg - -A {i"o.c elh rida*\ poLea,rre-
+cr. s = o?!or i]a-^1"r de''adf"r ce -Frr2e-
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a.Ble &e
fn ^
bec.
opportli,rf4e.'til'o ce-t JriJa
*en * = ,49AP
*on sd -- tcAP
ran 15" = tO r(}AP
lo-+ a- =- 49
&: l:{-3) - I O
-- 4.3r- cr.
.lt"'2xr "t tla,il*ilrld : :f.3-r.o.
d& i-."" tel-cuaeo P o-d qf oob of |our" : l+.6:.o,
Jeei?hr efi .rhe a&l : l. a .o . 3 cD
p &+oos el- q-1"' t $o." .[o-p porF = 3"2.q. = .CA .
ten3+r. oF ^hddot, c':,.LteA 6( -[a1, port : f e., : EA
LaF d tu Jtre- aoq.lc lc-tbte^ded \ *?"
ot- ,lhodow +D fog of ff9t on; -Lo-p qorl:
Ji., ct$o.re dc.fa ft r?,rertoteJ ig -f€.*.'
o[ t'k-'" &! lhocr:o. ,.,ftt, z4 --1d.
J-.*.. {pT. O gr&pqareE&_grir," lt="o
t oJE
to x t""13 )-If, -12
ta^ 11 = co_Ec.
**n = L,C l"-'-r 3 : .t) (---{ A4te"<*-----."l
EA -cn
a l"L
+ e-3,)-:9:It'b
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-?" a geq.*o,,o1 = *g
EA.
lan45o: AB
*,ePgt"t
4'c,Ag = +,e.o.
of {"-.'p po.t : AB = 4.s.o.
f^ abec. .r aBe4.
LDEL '- Le'eA
LI,LI = LBAE
A.a r P-f la"?h,rC
Aoec -
TA
EA -C-A
= <. Lco..",,oo t1^qL,J.
= ?d.
od
be_gc_= Bg+ ,
DLB&
=!QB4
ge
Ec-cc*trA- - g" 't
{"8 - 3. r- - 1-4
1*8 RA
t.L = t.t"4'8 B&
BA = t"6x+.9t.L.
: +sm
,hcJnhr e[
!r"-ita" -F-,uao
,lePpr ot .[o-g 3orl : f.& co.
Jrefght efr ffi bt PQ-.= r.s-" = AA1 =Ber
J}.\-L bui Ld I .a(
eLl'wahm -ra-od
CD " 30 'ro .
4i"rt poi.ts B Le.4trlA.,-'LL sL(U
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Page 23
let- *,o
4t-Ar6t a
DU;A.LL
"b
mov€J fo p' a_"d e.dz, p
eL,zo{,"a- f-o" Bl . p 6d
EeYruo.n ott""rr.,t'.o., ?of-k_ ,1g = At6r
a t,F,,.^t"l ,% rU 1"-.
J_Al](
. >g.g **?,15
_ Bx_v3
= 9.s,E..,.
:c= 2€.sG .- 9.9J3
_ rqJ!.
- lq x r.+32 =_ ta 6..
Ar a-"d e.d?,, .porftfon cl,o^6e| +t
},=;€f-+t:b
'fiai!flhF ot t.rrtdfr? aLovc_ r-4c _c fqc_r
Ce = cb -€D= co - (ee';
= 3o - t.5 = 28.5.o .
Nostr'
tof
?n
g, &-.
G r\LdE
* a.' ed =
G=
=)Y
DPl.Laoce
.Ih-e
dq"'r,!6 hr
ce_--ae.
> 8'5
oLov- doto-
or 'ii^owo
a"tlel +".or,^Zl- i$ of .TrJr-, a,"60a &
-l-A A C&rg.
*ao3o'= Le4\ e.
)8"9-*t= >€.s,Q
oa:orfl;- af,rt-
*{i..ce-t ciae
.oalKe.l *o"r:r,,r.L tu.ifd p.fl = leJQ "".
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zg.
[.F -h*tlt o\ fot-.:er +e= ''l-i "q--rvle
*ocor r
-4-qle t.( "rff * fT of Ahar{ot,,: -Fo tog
c< -- 6 90.
Ahadcl-.: be I 1' r'r. = BDJ-a^3th ol.tl
&.A+{. D \ r-L'odo- 11 (4: -t4o) .' [Fv '"
ai1le "-t ekv.t'ooo u F= ad'
.Ih, aLa,e- d..te ,or v e q.' .re. t " J p"
(t-". d1 abqo.
+-".-flt" &)e "[ ,k-,tr,^are,.ctcrdeJ *4" (J e !t|u\?a
Cl.*+o<gD5-z<-**J[
Lar
Lrle.
-le'e
Id-d ^ Agts
|a^'6cf = .1,
-x-
"r. : xJi _O
J--- CDr n
.!, .
fa.p=
*an.:c" :
4qEL'
.h
Jrf +orci+o: +fi _,(\" \')
r+4o= $€)G)
2o JE .o.
loroa- = eoJi .r.,.
l--.It*^e - ryal;C-_*" I
I +uio.r^F<t:., I
-heiX h F of
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2"4.
ffv'"-h(,'Bh t. e[ bLLftd-.T'? . :o.o,= 48.
.lel J"e,\l't e$ n,otae, atr*ut t.-1J,%q =;e,6i''r ", tct,:.' t b*gtd% = Qttro;.o, [{"o..,*"81" rt rL,,al f'", oh **
"h *a-oc, x= tsa.-*o4ie ab elewotPsn "r +" of -totoe. p = s,f .
lef cl&la.a. Lefr,i,ez.' focr,r, .Q d"r.'-^t%. 1of-l =
aloavz J.,b- ,i reg' cre-t-eJ P^
at l.hot"J,r.
D^e "t iI}. Rcl*.r..r *q[.-tLt ^d, -1n""^01. ,i p
!tF{,
rt-'?.
,,FL't ^,
{o.." r,h {er"
'N.- = p"
;1.roc-Jl = 46 .v'
5t '.n
(+'",
e
( 'o^rl
*-nn 4 = Ae,1D
-, ''t1^ 4qr __
II c\^P = CA
D4.
=l -ka- 6o" = 4,r rrr-"'
. 4.,tLA = >..fa
=i .}'- zot€-r)
> ro tJE -i).r)
= )o I r.-T3 !_?)
= >Dx D.t B! .
= lf 6-+t .'r
Zp-
:L : 2o., .
4e,'6i.r ofi -forr'r"t L
= o Ppodlt aPdc
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I
I
I
2.5.l"r +,cQht of r^utu,stariacr f.tLl.h ,j.,_.= AB .
+le,?Ar.b ,b fdu k trd,T, = I .D. = cD
-togre ef d1.--s'L "h -ttf u6 +-t, rr,ird.\ < = :o"A-Vte ofi depv"rr?r. of tob- o, f"1r f".iLa,rn p = tf.DPri-o^ce- teta:Ea- +*'o &ttLa,''tl '= (>t' -4 = g9
-ztB = 41 1-16 h'r x6=co t-e-r Ax --:-
[','nxcr ri "- ra-4"1. fn'te ='dl "n -t- B.n
46: (at s)-o
a.
Ix
Itr1.r, crLaue, ,!4r".,-ffl^ &
8o .{tr do,- ,b ffg*""
t?"rtnbJar ,<hot r.
B F= *"
-r.1F..,
$ L Ax&
ta":d = Ax
t-71-
3 + q e,)
ta. ra" ^ A8=f3)
tL+ I>t, .(\-^
BDn l= *r=eI,
+ cL-tg =:{- =O
) o, # * J::,1 = 4 tJ<ti)\'-<- !" ti- +[J3+r) %- +(a-,E)-.,. A€:ate = +(A+g-
(].cr [tiho-%J u^]ftd.,"^a , 4 {Jc , 3) -,bet:,,e'. L<'?w$ff 4(:. r1r.,.
Or"O
Ir efoN"t
D rJ ft\rc e
c^,
:L= aJZ --ri
\,fAhF &.,"(}tl4 o!- r?-'ct..Jed o"4l- 6 o
,h
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*e r +e,"61-,r
6et"3Ar
+l.7le-4-? tc
.tcro x - !6,bL
ta"451= +,DL.
Dc = +\"8.. r
Dc : \'-o ^.-6
{*o-' Q *@ d- "1,+r.s
ob StQ-".
-,"A}.,h ^81"f-6 [,'lJ 1.1 aj[e & B
ol_l3l!_ rG.€fcree-F rfl4e-
e ["...t-io, eh +og "heLc.rat r"c- oF tcJr! rdr
oF ordcrlol l-,e 'J..-lltAFztFr.re = l- b.r.crI
€L
efr
At-ab?- d = eb".
F = ,td"_
th.WJT\-
"ioh
s?.,
aky..,1io'.-
l.
J6,.
datn
l' r-.+*"4?1. crr.
s- ap-cr z-,|-eJ
aJ z-Lrourg.
Lants = ALDc.
fcr.- ad
DL=
=5il\/
-r, + tjL
a-r'h\.)
G*,.D = .h l',.g
^Lr:) =16{' t't x 'l:-r r€r .l-.*'
of 3e dtrt-a L =
= o.8[-t]+r).
D,8 [.l3 ir ).-n..}e r"Xr,.r
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Page 28
)-1 .
let J..c,khF
l^li.J ii. ol-t)
*-atu o[UU
l\-.,rtz "ltCU
tT-
to
l.
J6Z
o.bov"
ofi 1;otozv : l-'.o .: fr@
r'lve ' lrz 'rr\-o = gg .
z.b"ation !'o- tc-k "f ri"." <.elr-"ahl," -{-,- Zo.r> &LoaL{ JFr-
ti 'Y''1ov€ r F -- ao". [{,o"^ o'1.
dcrt a rt reprrrr.,t'z.l
d* "| {.3--' c.r a|.,ot,.,.
#qt* o,rgt.. t',"ar.t . i^n t-',9."t*del tc ,$ o' .[ko
e o" [4-* c]
t.6"L
5. A *!3c'
*ctn a* : ,48
tsc.la.
6oo = 4,r
f-, a *oe
fa-p = aeDE
ta-.3,.,"- -1":Lt)!
).+ 2ll: -l-.li -ri\t:,
>L
6= x€ _O
f" G :+ Er2o = x€xf,:? r+2D:3a:? lx: 2p + x=lD^r,
.-1.i = xG: t11;r{1i = ro6.o.
Ae,ogr.r €l -h"a rJ.' : to.e.r-,
ti.ltt ") r-fvay \x, = to.o.
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.
I
2-8 fl
tove rr le fehl "h l>ur-tlJ 'P.7- = r ''n = *6+ferftt f et- c-able totoc' : tH''o - aD
,-t6a.
lrr
+-< le o$ el' q,lnoo^ ,b a"p u[ -lou.,'., -{- o-- -t op
ci tril.l'h d=6a"-A"glc "i dep.<rrf--r of- tdro. r,iof + builal"n V= +4'
t,cr-ro- l.o"tC
o,f,r.,a drrta & .'- eg. e-re''feaL
{*.- of {i€"" ^ 1l-"''
CX -- ' :t'..cD: Dx +xc
-LN A ADX
tan qs" = of?. ride Lxa)-Ac{j. rtde tex)
!' z axc
1<ro 6o" _= -L c_
AX
€-a+
I 1= I J:.
= 'fl(i *,).n_
-Foc.:ro -- =+f,lit r).o.
:7 AX = I "o.
"^
tnl LD --:
x'\+q-G {- +
+, e,'gt"t o'i c,r"t,k-
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Z1' Vfwcn+k,gbt oh I'br,i -Aot.ra = +8.',.
-Agte d .teg'.rsio" o|- rl.'g I x
-Agla c:h d.,fr?rr;o. + ahf€ z P
IE obo,,e Jala & rg-oe.;73f. j *.". "il {,ft -".e a.r &l-,a,o .
LLI D,\ f a,.c. Le F,,.x e^ ot ,?. t"':J .o = 6.5.
= ,48
"for"r -*-\U1n f$ o.e
'b.r Iu.1eJ ,r11. ,'c o JF*
^
J-+. F: 4s
c-e.
+c.- +5" - +gEL
Bc -- .+5 . -O/a\ C) /-\C' '" (rj xt +5 = +5.43
{ = isLJ:_\)
- lr r( f-oicc te F14a.. th."-aI
)C .')
- +5t.4..\)
38.
+\'
Lqr. r
_a^
oi
fcw, go" -
rcB.+5x-r8c.
FE;.=-.lli.'ta-rar| -+df tt+ rJaz,l
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Page 31
30.+^3ta e.bt 6'f,;en "b 1rp
-Lot oar : 3o'= d
" [r ,, o l-,."o. o ! +r;g
6ufttf.? = a""=p.
+{o"t-'t"gl" rh{oel of
Ttr! abova f'^ 1".,-.'otr",r",
d,"fture o,r lhoc.r.r,
-4" aAe,D'
tc".r lts =
-Fo..6o' =
Fs> -
, . _p".
?+g
AD,
5!-8D
5a\1.<
{n3
"i.'t
-tle&bf of to r,-re " = 5D ro.=.48
-tte ."or-,t ol, t'-, i t'l '"-9 = t -ry0= cD.
.7- " ,bFt J, ,'..-o /, il, ( p o[ JLt
,or I tL,- li^"e -- c,r par +- l:.f"]| ;",."._k"&
I
1"€,iH- .'h toi l.l,lU =
-ra CgD
+G.c(: cDBD
Tar :d = 45oG
J-= 6o r
rlz rA
=593
of 't.,,'- 4-o-.
tc-'Ed r!"
, 6, , rbLrL rd r 44 +y c)6
d"_.^ "h
3.t.,JeJ ajL
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51.-He ig hr
4.2,\e
-Ajle
6iwz', bo^ks c,'t.- Do qgpo,r?E ef.1e5,
Dr'r l-.a" c<- lxF.ure-, t.'.'ke 6,s-= qe*
,fh. o.bov e, i.{o-..,oht, 11 .,r e g"re r a-f6.1
S +"g*". &i
+.t
oF .I6c, L;idqe, : 5('-1. f lte)l.
Ae-t>.n e *toa g$ L^- O ,a i. .- c( = zo". le,\d eq"r err.Ioo o| baola- 2, r'- e p = 4a: le)
B.4.
.ttL {r'--
^ r'oghr o"^9l.
oh -[-hs i'rcludaJ
i[Fa o
ll"ot -,o.
_{-,t\.<ltoof-, 'tJ
( oaz
a9 \3o- \
-\B'
-r. A AF,n J- aAge,
-Faop : AeBeL
f""4S = ee_BBL
BB,: fe9
JoG t :<o
solG+r)
*an <o
B,e =
ACB,g
-3qB,B
Sofe m
Brg. = ai8+ggn
-D,lc to., " Lr kr.r^
| #.o = opf ooil;.,"a.
- {
I +uincr"l r?& I________:=-_ I
h'.^t r = 3DtG r() r{)
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3\.
Le l- $c^-,o pot-
G a AYe
*a. < = ABBX
to- 6d - l'\-
,q€ a
Ag:-.D
CD h€ akU
aciu ret +€ ,bh f ' + '
f>i.t tct"c. betcue ea ?ole , BD = 8o .o.
kf X !a PP.f Letcr.<,t -lbc -e f'. o,,. 4 -2- A-,1{a .,, e [r vahfll.' oi *+6 Le d. = La"
-A*jle "i ato vaffor o[ co k F =, -"
pi irr*. tt pflor {--". Tolz'ao' ='BX''., =\x;
pir fo-"re "6 3"t 4'o''-' l.,la 4-p =1Dx '^' : i$p-r 'o
llv oj:>o,te Aclo & ""P"'*-t"'r ^ \ Ie do'- oi d,!.,''e "'' ^*"-' *-i \ ,/ l, -i- ',iu' r''""^'rr' t "' 'i i \ / i
Fa l^"t',at" ^€9-j- 9
.F'n f1^"s = c;$x'!-{iai"^c"-rria''
s^ acxDfon B = C P
' lo-tc,- 3o' - +r
go-f,
!o-, - 1^,.1f
*6J-, = >LJ3. .'-6
'% Ci =2 Bo -x- - x.r: [-G) :> 8o->c = 3x.
+ t*- 8o + x: 2-D. $- :oG
.l.,e ,!r"t "fi g"l ur = 2 o I: 'n '
l> rl tr"ce ob p. I- r fo"-- Folr- :L : > o '"'r
Dior-fcr,., c. o$ Pgt f"o'. gole -:- = ao m'
g 1- X (€o-2, D+8o-o+-.J
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I
I
il--*-*----,35
| 33.4. ,"1r.r of t" , e AC -_-li
A, -,1" rri Jar.',"ri,L-Jv{
{-c'la oh .1aq,,11P6.J!U
g,ct b b.re nol, ^ B'
'J-t,"r,,^ I DlP. a \? r )..)0'
ta. 6c"
€8,9
= &q_B'E
B,B =
B, 8, -.- B,B 1.e8, 1
-{eaf 4 :6p'.
{ezF p = 3po.
20 .o.
oI gJ.
"b ?"tnc., te
L
L
: Lt,".r1.9. "h o&e" = BrBo
= Brstga^
,q, obcva I Xo_*-,ot,'* ,i qYeFe!€^t€J ,1.. {""". ofr {g6*cOd Al-,or.,o.
i. -thr +.,\1" , i{ ooe
c: oDDc([L atde- JJ =-hc.-b rtdt'
2p_G,
Lo ^F : A{3
8's,
fa", :<c. = !,et
*,
B% = zoG.
29+ zol: = 2o I r,+z'1{1 ' - l"--lL .13 J
= go ,.,.r/3
= [email protected]
:€oG
\^tLl+c, "b
oll-,",;,olz,.
o3]'or i 17- I iJe't
of ,"-elu.leJ a€t & 0
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3L.
. 4l rw€a0
rle,'4lt rl jtaa,tl-L[ = 1.n= 131 .- ( VU
"{e F +-e,'5nt cl tourc" = \'.. -- ag.
-4.gle rb etc vr"l tin o$ !o-tr;o. o[ {ra3 r badl
-A.-q\e ob r {e vcrl-r"cn D]i +op "i .t la3 rta[_$
f o'lt "b oka..va F rgte., to- ' p,
fi" oto,^e datsa i lrep^ner e.,bed fl -l*.^of qf ,'g "."e dr al,owo
J; ',"9t
t a',51" **r"."n3r.
Jtrz Frc0utde d ^l?t" '1r----- --- ----It,."rs = erori'l-r- rt;, I
i -+.rl^ca^t rPan, I
fcrocl * 4gA?
*zro,:o' = {tA(
-Ar= r^,J-3. -6){-.- @*@
*Je: -h++
*'.lr-]^ =n{{Jr_r ._ I _> q.
.i , ra.,trl -j vr?,
= +r (e+t; = B.r[d. +rrz
"1, -l ou-,," - 3'{ (Jr'r>-.v-
*= 3oo
F = +50.
'91 o..,.
O -G-.
Jr ^-P +L
r - r]t+AP
4r -- A F:r i _^\' l--/
I
iI
I
II
i
I
I
I
I
I
I
i
I
I
I
-t,.'!r.r
l
RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in
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z1-
Let
-Le 1g+r, "t llado,.r t" 'a'-be d. - i5"le .,.r1r, dr l'dot: t-'?t t I c
JVo r--dlua ntliFuJe ir 3 = 5o
|-t +,eftt,t d -1o.-" Le
k
taa,I'- 1,rl-,p- :-un attri't crA z
= gD'(r x -t a ).o u'lo.
t'1"'-., = -18.
-.F"*..,fuJ ,P.-f,h-e ct tor,^e
tf d."g.."e
,".-' {o..na hote-
or Al.pcoo.
i^ "'"S^t -1 "'hr3la F e + rr.,e
a?31€ Pr s "[[ie o
- TL*j,b-4i4sA,Lce"tlt&^
!i. -+ec.
-l,," "r :-fo ApB.
-Lo-' g = t11--' {azr-a"j €r.
ld-to^ 3(] = -Vj2'7! a-
L't-t(1 ": t€ -o
-tr.4^o
-4+.B. '
=4a' 4)
o P., => zxr-h = *'Q+ J- C€-{) = 2rt.
'J3*t \r?-1 I
: 211J3 \ '\.- 't*: >c I J:'ti;
.1.elght of -lot"tv - >cL.Iar,)m.
,( . | ...+e.l
*=f5"
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t-3b.
I.e t- AS V +4AbF o[ t;oe L
po,'nt c cr"d tog -tou cl-,ar $.ro*nal
-4.,312 -,a)a l>x %e o==o..Pf1tra.ra +r-- {oots o$ F'.o. *.e--Iouch.r.
6vou.r\ = io..'rFee -
.Ap.-ifu o bot,e ' ^(a-no F,"n ' rl
J,%u'e dl al"oc"n.\O
,he&hl- ol I'ee = r4G: Ac+rB{v : Ac -r- ag\
t-a"5te
"ftrt +x\ta, iL "* .fi-Pr s irftn
LL
aF
L-(
^ll1
token aF
3oi. t- qzl'.e.e 3t-
BrF----_.2rofteA
tbear&^.dft ",...",
f6y1 36' = 4C.
da'tos:o = 4€l
Brc
Ac : -!-!l'' .'),G.13 - tn=- -g'L
Btc = !,o m.\e
= .!-L r- r',(3 .fe
= 3o - roG.G
-Ag = CA tagt
Jo.o =opr:<rri F alde
'Aclt"ctc ant sr"de
+,e ftl r tb -1"2" = l oG rn.
i
I
I
I
I
I
I
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.5.l-.
Lc.{ tr1
-A€tn
si.6 = teB(:
*re t'q h I0
38.-r-'aPBht
+nte
4n,Sir to"ce
'tfu &bara
{,"0** 0!
f- lghr
ob c.lble co-rrctzJ to Lat(oo.,
'f fqr t Sa Fr?- of c -r1. r.rtJq= Zttr,,lad
CYoL{.,d
= r.6'm
= -'4g,
r( - 6oo'
lleftbt ofr Lcrtf co1 {'o.n 6ranod
,[C1 crbore dala Pt
{ {?-"" or 'thcLlJo'
J- :rl9 r. F t'-"c."5 t.
i. cf ul e a oo3le ir s
3 {"..^ "r-
-7rv^1ad g lU".-"
o.€ "h
.6en
=> 9- $- + 4"=_ Zt5
4 F,attooo *,"-^
0F 'trft = Bo-o = "rBo[ elcvah'm {,o.., r4o.] J_, cr :o[ at-tvnhntrr .J-.r.., Man:, B :
Lttt^:e,e- *.co mel - M,Mr.
: AMr t 8F42, ,
l";[o.-..a t-,oco f, wepve re.rteJ
{hoc,ro ,
oogta t-.ocr,rglc sba o|, Ol.e
o.'.'21\e ,i o .[{eo
1!g = lo4.5t:.n2J
flroctoJ : lo"i.5.& "r_
3so" lvr16e lv,J
3q
*&o = "tf*f trtoE
.roo* it-, *",d. 1
{a.{fil
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40.I
foo or =
*Ln., 3c" =
M1B =
ta^p .*
fc\,6o":
8I,4,_ :
4uBH-
g!BM-
go.J3
8o.fe r go _ Aox a_{3 fg
= iie€ "*tr;.r,3
3q. lerleQxr ob pote. ='-{-'..' : z,r-tr'r a[bttud. $,.,_,, ground,Ie.,g+t, t:b ,cl-ad or-. ba '-L'
Xivr" trr.al- -L - t-.
4s_MB
SoMrB
8o-B
M'h,L = Mrg+ BNa, =
D,lFo.ce bnh,-lee", noeo
+*A" "i e0e vcrh"-'
lfu o-Lo"" dort a &
ob {,"3-* zlJ d hoc*o,
taoe = 48BL
cf -c..1 athglcda be
rcp-rereoled F, (o*^-
:- 32.6.6
e.
r,Av
.1. -iq \ F +*"^..Sle &{ ,,,e_ "fi-c[ndeda.6te&oTLeo
pfFcuYlt,tide I
-t-ft1'a c €-t llA e J
:| *ct.,€r : :L{.
_/ -rnnF __ _Q t" +rr. f]:* O= +a# l\) s4go.
ch {rL..r\ altrAtrde & Jeo,-4.oVIt
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An.I i -r
:Ann le
{l
-As
ob
ob
Le trL,e LLatLA P--a .
clr va hoq, {,'-- 1Jr^- F I F,q ( *6 t,.r,.. r]eLtvoft"o.r *,o-, por% l- q I Fi.re. _< Fa l-,.o1 >J
q = bo".
F=4;1D ir Fct.'tce te h-.,e<o F,?alt-oria* FeL = Zok-.r.
'I[, o,Lo,te ron {o,.^ah'o., & reg"ercnt-ed
ff tj ".-""' "b -{ i6."c 01 r hog.,.-;
]i -pr +.'atu q w "'b JR.
"?. 8ce ,I[po Xto. a = .,4s
A?.
L&.6o : 4A*"
Ar = 4\Bv-e
O"O + : -ag /t*-,|-e\.\,f2.)
AB = zo (z(,c -r I
-A.rAQ = ft_ a,a
20= -€(]ri+) +
.<l-,o utd dz^d i l-{
Y.-r2, L.-,.
to-p =
*n-.-1s"
AQ=
ABAE
Aq
Aa= i;$"* = ro.r3(J3-J) =,p(3-Jg
lle = lre . tc,l3_f,3) : 16(3-r"+321 = |z.6tL-n
= lO^ O.-r3,- :. W, +"32,L,.= ro (.t-r){s€
Slah'{:rr a
+n -kavet
f e o.- zl.-d {r; , ,.', !,a *c
+t.RD Sharma Class 10 Solutions Applications of Trigonometry
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+1.
fhr'ght + rhip f"-"., rtzot?., .!-evet : lpro = -Ag^
-tlr'te 4 ele vcrhoeq "[ *"f "b .linh o( = tg:-?+"A1" !b dtp'.rct"r:^
5 6.16-- of (t.f-6$, A =_ 3d,l'ef6r't "l ct3$f 'co = 'r'm.J.'iLa"ce, "t- rl",'1' -F.o-^ +*F .f t-q:e'. c-t.1F.
ne,ir"r .l ,(,'-$i "[.^:l? ,_>..---itrieo -1"e..",.r- -b cr,'ix- = p1+ra _l >:o-_- 00-rarrn I c \)4'o-l
: aloou, do+" fc ,r7,era-t.A l_----' ,
'
': d.* "l d.ii',,. ot tlow^. D---------:i3
-?,", ,r!lr +-"ci.6le, f{' ,r.," cb {Fa r".ctu4s.{ ang rL &e . .rr-o. f*=;- rFtslE;
-Ad.'aeu "Frid.
-Lta^ +t" - CrAA
l: aAX
Ax ' ' 41' ".t
*n. 35. = xpAx.
-L = rov3 Ax
Ax - r o,,lE
L. - rtJ?.o.
o[ ctr'1[ - lor-ro-e = \otJ1tD.D.
f-rF..rr^ _+ f-1- e rtP65 = rce.o.
Jv,%'.ta)
d fi t a,"ce
t)-RD Sharma Class 10 Solutions Applications of Trigonometry
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+3'1
-i---142iri+
ll+I
lorI
l**l
+2.-t-|e .!rrr1"6la
4'xylc+l-etht
D&hr"c"
+le it3hF
+''llht,r
Jq!
.l.tr\e.,
"b rhfp aLove u:,iiu tevcL = 8.r' = '48.of etev-h""h "F ++ * ctffit+rtr1 a.26r" .
of -lzp-tr.oter o6 kf,to",>
c'f l"ft{ =- cD
tr h'"eto {t"rop & }'itl = AK.
rt 4?Lt a tove- r;'og= C_x:'Ar-n
ob hirr = krrg) ..,.
l,ftt g= 3Y.
*a. p = xpA,r(.
tCtn3o : g
4"Ax = eJ:
C
X
tt6ov- de*a F,L ,reyerc,:ie)
4o-- o$ dfqc,.... ar tlrltu",^
ftrr+;u6u ."f c.p, "$
r'oc tutdad a"6lc- 8-r o
tc".. x = 4^
-fcr,-r oo'
AX
-arr.AX.
A{-s
-Q=",3
8Q 9 .r= 2.1 -o.
A( = 8G.n
+,ef6r,t ch otf1tr'9@^r"9 --Dl ttt"ce l.ra Fr.rt c^, 'h?tr e <hP6 = 8.f:'o
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:4gte of &p'"srio- "fi tf of te ".pte z,
J-e fo hr oltv lc-.,ela r [$e) = co -.I-
ot t"n-"- "bz CcD = r"r.,,^i
$o = rr, .a.
Y eF-' er e.l-zd
a! rl-'q-.r). c
o.ra ol- l, ,l,] --d'Fe o
D
* = 3oo.
F= ed-+.de o[- d aPvesr rqc"r
-hefnrr crh t..^dz
l^lfd +'. sh #ve., E
'ffu otbore- datFcr &,i {o'--" of {,96*'"
3" -,"grt -*\1. ft
Lt ata r( :
'lc,r 3o
LA
AIC,X "
"= tZCx.
= Ax.[i.
Al("tl = ->
cD=
l,J icllt,
4.,%trt-
E(eXB:
of-
ot
48- Ax
t..-pL
i loa
=:-|-o
:6-r-')3
- 5o- Ee3
AX
50{)
loo-1
te-ytz z,
fict u 6 a3 ag"le ,1 s,
f&., s = t:P po{flL- t?&.
"4djac e"ts < Pde
*ctr g : 4gBD
-tar 6q," : g6Ct
cx:5c)----E-v<
F=ao'
4^t.e gD = dx, (]D > gd,
l
4.1 .
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+4.I,ef -Ae'5rgj2..,3 +raqctt.J 4'o ",-. A -!a
A.r3le oi etrvaF,$q ob ?oP-l A d. =
-Aoqla "b r Lvo troczo o| ge,? f e
J"ei3l.r o[ ae"opla..re. $.,- 6,.,"-J =_
D&|o,nce {-"6-wetlcd #- tg recr:48-pa.
6cl?0-.t;;e!.Ai. -_ ge
B.?+29
t q .4 ec(.
'13 :t+Lt
._0n,
"t
&"4ln
velocl! (o- r -rpecJ = -lSrt-n-ca -\o v. rt-; 1t"^.,.&bov< c{a $a r! vegvalr-1t'e6( 3 lo'.-.
<,hr-. ar {Lorr',.
.,.h;t I .r'2,-^ qlr c>e .l yl a\-.1 \J l)
(t O "![^,\
*.'-ts = og?.?tr 4&9-{a ce ^t-riaa
*o-- < = ARXF
.la- 4e" =
XP=
3Q. =
Ayeed -
Soooxe
3DOO.,-r)
x q - xr
FA
3". i.,.tel
+o-p = 3qxq
ta^ 3d = 36rp9xq.
xq = 3ooDG
5OoDL/31) rir
Sooo LJ3 -l)- l5 -zcox o.-1 .).rqa. 1 ""lL<.
2oo CO3r)
/,yec) 'b -*e'o;fo... = t+a.+ -.A.._
+eRD Sharma Class 10 Solutions Applications of Trigonometry
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4t.I'e r*^gla
4,13te
-4,'oe\a^c l.avatte) -{' Dfi 4 +o g,t
et+valrbpo. ol pogt A =u"at-a va LtL- oh PoP^t R "
4g
t,.h
"i
-6D
FQ.
A$*
"hitAc n
=1- 6,".,rle
-Fo^F = BCxQ
la" sd= t
xqxQ=€L-n
= JE-r= zu3 ,f3
-t"l
lo r
6ox6r>
z\o{-z
= 4B v.,-.
-- Z'fz x bax yY
L^" lt .
4"&t"r €b ae'o3\a.re {*o"o ?x-Du'f, = t L'n
.D&Fo*" -t:-atzatlcd P" to LL(\ =
.ape e.t -- .} ter l.a oce -+-.ave tt e.l /-l,Le .
JFJ alxn " dat-c' t% r76ra,-,f221
{ Pq",'. ou r hcu.-r.r '
5" -,!1xt +.\le, ,"tr o'e
'-[Ec rsocluded o-rqlc '1
o.,
o- oFpcfF riq4s
-Aajac e"h siJc-
faov = Ap,PX
-fa,-r 6c)- = AP;
Px=
PQ -- xe -ex
f-peLd = ,Pq
-lP.oe
fee.{-&*oylon" = zrro6 L" Fl'.
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'*B = 4,ePg+ o$- to.,:.'" -- so"o.
c)^e- + F.,cl..Ja4
*a" < = A^Lx.
ta^ 4" = AXCX
Ax = 6-1.
.LLA^F=
*o- 6o'
gD -^LA &cD = g(.
+eBD
=5oBD
5o\.4
Ax = ';n=
-r). : gD.!1
cD: 'q8- Ax ,- Eo- 5pa
= 59te re).?-
5!C&:pJG
+'e..!1t"r
bi ra,t. "
DF bt-uld.q.,? tpol"l = $(: _.i11".'r
tel'r.,'e-"-, pota !. *oL,:r. : fq ,-.. ^
cr,: t"zrlrr an V-Va.",fuLpae)
-A"3le o!- .leg-<rtro^
'/\odt( $ Jep.zrrt*e.,
t\J' r,.brtze dato- &
{ fr*'. al sLa'oo
il-, ,*!;r +-Po^6t"
o.rX re P-c o .Feo
d *"f .f Lna,."6 N.=11".
'b tptl.'.- "b t'-?u-t'-U p = ed..oF..r..,t.d ,"..., 6o 4 p----, oh
l+"^" -- *"*tt- rltTI 8."',-lr-l
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Page 47
t+'D lr hr',ce &fc.ez. *< cet = Oo.n. Ceol.
+"Ehf o[ ^LLE)a]
tye,c, = 80 -.-',. tcDl1"; {e.'ghr o$- F&rr +-e-" ='l-'"- LaB]
n.gt. o[ JeSr e-lr fo-, f." r-c.,"} t*."- top
ioy a = ft*'=$fL a,,r sve r,o^ {o -.-abfoo & t"p"e'e -teA B
Ctl {houoo.
t =,!c.r +-,}.,Ut. 16 o^. $ Jkr.Xc(uded a,t 14 $e Grv
Ln^O : cPPol' Lc lt.le,
"A{io c-e-Fr ide-'
.'t\ort C* I Ag, Cx _ BD = 6D-n.
x.B = cD = AB_aX,
to^ ". = _AxC^
I-ra^ 4s"= AX :> A(:6D.q.Lh
Kg -- CD = SB-R{: go -to:: Lo rn
fu;- 4:".s r,..
{*- oh t,3q
I.. IatI
I
J=. ".!,lrar jgt,t
&om
2D.o-
$+
Jt-co",d t*ee =
tY.* tee- =
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tc.Ab Le fbe, ttee b'o^
-{-ro- d&ha .'ca '@' .., 4o.'( eoi h
.,
trhr
Ine. f"al uJel atqle-
f,L o."D
14e
d"",-, Ax+ Qa,
*a., < = Ax
t-xAx
atb a .A\ colBr *e)
F-+t#
qiAXx+t.
).1 t,
Fx
.{z t e^
T
J-^
cDtF =
ft&
aDt ( I j[+&
IC.T L : A)( coF,(
6*O=)
-t6; * f:c+at - ^r cr)tp - Ax.otr.
Ax = lb-or to-<, ta^el;_r-^F*
a?ee- ,--A.ogte of e-tr1oq.'.',,
-+.q le- ofi e Lr.lau"c,,,
,9, .Gr,
ItLo
l*- x aF ?oBt r.d & ta"ca ,b, .., 1-c,- X"e"-
Le p at- pol.,Fq.
a-bove- do,,fa & .'-eg"e.Le-'lad
P h {.tA*"" o.r rhg,(,re.
.rb!.r +-f,-"?r! tFHo eBF> a,<-{ X
+7.
DPPDTf L- dfde-4d fo. c a^t r Pa.
RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in
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Page 49
+lerhbt- "h verFfc.a[ toure-
-Angla "fr e[ewahL 'b -bf
-4€1. ofi eL t -h't " o$- top
frv, abw. ,1{o.-o kq.l ,}
iiT*"e 0r. lhc.,o.r,
i4 "!r"r +-,Lgt., o." o[L9-aludeJ c.nlL .!' s, fu"v
b'cr co Ay _l pe. ,
qa = (eq-!-I Or 45" - _a r.\
^YAe = .4y
-/ rbr-+o =Ay.
Lr
= Pe.
{ro-o X, o( = !oo.
*.+-" y 14"-. a[,ove, *) ,P -- 4so.
-t 1'r €1e -t,'J P. +.'_ o h
X
.-4r) -+o.go" = Ig
Pr.
Pr= bnG
P0-+o=pc€
Pqt€l) = +oJ3.
zD€LG+r) -. zoL3t .^3),
2oL_: rrg) ..,.
r 4.,0 -_ oppol'LL Jld.ta-Le.tf ltda .
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Page 50
lo.Lc F c-lc crJ be- cr l- -l-.,e ."gt-t-
.j""-, lat<. "levc[.
F.r". porb^l { 2ioo.ot-rI
of-' ctavoh'."- of, +ry 'f-+-6le- ob /ep'e<f"- ofi-
$e". Pe - tre' d-.n- .,q,.1 -Lpq.Jel AO.'f .- Ap.,z'-. y
PQ . lhr >)-.' pq'=6*,.,-rrj
? otove
, dat-a ,? t"p,.^r^rcl {r^ <--', oD X'b"". ar (Fawn
5:^ -b0..,r +",h^At.
on5t'. &e ntr*
fan rso = Aq
^Y
Pq
crloo'.,.
cloc' J
!\c.Ao,,-,
3".13\L
-Ga -tcr k cx=t59ty€t kc A)e
r.; ,_.nt^.
c.1te-
:) u26g= +,
"Y-)aLr-t,l_-r)
i--.,ee
#,^A xO $ . -- 'L*:- =)o.lA8 +
{ o"4<'-- 4_e' = Ac*pp'AY _^Y
* Aty = >.-.r C brx): +r z7_.
+ aY = g+,>x ._@-o
*L' = >x
5_oo o_ =2 -igl
>scD
t I3(r.83\)-.
I
i
!
1
I
I
A.r-,r630.83tat2qon
43oo. g"'" -
iII
i
:I!
i
I
I
II
wep.ere-,tzJ
r
"l-'efgnr o $
a to uJ a.bova la bc
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Let x be, fo,%1 ,1,, .., e t+er
-A-qle rl rL'.nlrbe^ o{ ,louJ,J v " -t)
,A- ri\' ri Jer.err,"o., ol rrocrclrt$
-f,aiglr 4 r l'..d {-o-", 0r.kq-
Pe' Le IFa -€flectpon t6nclo.,,-.-, xA -LPg, , Ae =,r,..,,D'il o^.. dl) rrottJ {'*v
rs xQ,
ta^ x =
O -o :-z Lu-^F- to.,n = 21,
l! A," qCas c( =
dqFa & vcgrcr <-^,tzd ,: 4.-* + d Jgu"c
5o 1d1q r
.LL.rsP : 3Qr
e.
+-'P = l-+ >t th
'B -.P
orLove- ,Lake-
{woco y_ : (.
* eltc cl-,"o.r 3" .!-ate" 'p.-FQ.
Pe' = pe
AF =xt1 * tq,-.
g'f.t $ oLre,rr,^ott$.-.
Ax- 2l.to"
F - l-o.a.
'tEL abovc
At l,L, q-, n.
i- aAe*.t,-"x = {-Q_
A{.
Qr = a<
r(
-{D <D,41
ln
Ai-xQ
XQ
ABc x
: -21, Au x*o-p_ to^,r.
rh cloua -f,.o- gop"r "f oke.',a,hL: t-'raca /to"B- lonV.
4,1t0.,,..
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53.
5r.Ur*k
ra t. +. 'L Ll Dl aer"D * roltac€
! te tc_wo -.,ttc I Fo.rr or
Jfu acvoplala. XY = t ywila.
-A.gte eb cleg;e rr ic," ob K -ir.o- F ' x.
,Aoqla oh .1e;'err '*'" ti Y 4""" t -- p
.fFi above da t-a- & "reE*zce"'teJ P" <o-- c,h
d .fr*". ar t hou,:o '
5., vrir'r 1.'ia-"31", i-6(!),rO
."1 t, ( ltvleA oagr. r q G\)
tc,. g = cr-'p,lflti] 'rlJ.-1-##jac.-t-s2L.
-tY o.ri
opr.orii,z-ll
t-ou'J.liifa +
-Ll+..€J .
-r^ -a Px Q
I Ct^ ,< --
XQ=
D.L
.fi"^
I
,r. pA y
-ta p = roaY
qY = Pq.+,'"P
!Y - Fq
F&XQ,
iq_t
YQ r 6Y = PQ " !A ?*a,.a f-F
PA
rq l+gd-P-lL +o.,... t-pJ
= _1C.l4- l a"F_to'a .r b-r- p
ob ae ^'oglzroa = 4.^.: t ^.E ,--? ln"lan< + fur"p
1.'" P
-l^,e,%t't(j
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54
E-A - -o--- nA; pr. * l^,,"gr^r- .r *e-A^gle- cr$- e t"va tic"- -f-A.-qla ot= c L"yo Ffo-, ot
&. a[r,'," L q*.-,.af Pr" r1
{J6".ve dJ ALot:o,
- - r)DDri ( i L! .lL de" -) !-*liac e"t- eia..
C- v.'gr"l +.Jc'"gle h &\€ ob
3, c [uJ eJ o"1t fr ,s , .Ifu *
'i -toL-r". +e,bht_
B '4-c'". P="4I 4,o- c =F.
"'.fY cr€.-\t ed I {,r-*., o}-
P
QX.
+B
4eQx.
D'ao $x -! -AB
54 t@{
fo,"p = Bx
, 7q: A-t,4r=
--t-r A BFA
tan<=
= A6-a .AE
| - r.}nB
o- tan 4-ttrrr r{ -ta.
Qx
+ to"p= 4 8- ,4xQx.
916"13 . *R -a ^| _ -{rlQa.
e=rID 'aF
a=AB
-l'e,it"r ob
DIr Fo.rcn t{*
l-A4e
.trola -h^a- ----- ---- 1tr. < .
e>r:49 =ta"xo
ta. x *14^p
po." = o**ltF.,.^r_r"^u;
porF ! tor.'zr . .lf t*.",{ -lonF),
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51, Lef {e N4 .i-aAde, '".i+i-U 1 ah
d fo fi'rou"d'
r".ctP.ol-.tr-
l!i',e..' f k {oot. ft 1xrtldJ ffiiesgl- J&t-a"c<- 'cJ
lc F BBI - \ hl .o c.,rJ Aal = 't '-o
Dec., a,"6lc of z Lvze Froo" S' '''" et = P'
{\. aLorc, r% {o"".,oFrqo.' & n- eg' esc^tcd
qf sq u<e aJ {\oc.,o
Lel Ae_I A<ou'n
A'?=* BP=
f- aaee'
S;n c{ = -o
CO.go(
g a rie'e
E
-o
r% tro"..- oh
Ag = atetL
de
'd
_lJt"^g = A? * ci^g r :r- _6,I A'B t Ag \)
cor p = B'P :? cl]( ts = ,j *S _@" -FB' ' +ne
si-',a. g+AB
Cose( = -!-Ag
sinx-s,%g = t. AB.
cosg - colca = 4-, Aa'.
co!E: 's{_ = a3,?'a -Irbn p t
AP-Ae'
=gAB
o*o@-o
/=\-e,-@
@.Re-/
Co{o( - aa{ b
Srr)p - Jl; d
+
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Page 55
55' LcF Acr!7ht c$ *t..1.' b" 'l-,'.n.: Pe,
*oVie o! e Lewcr lL"o.' crF loEF A o-' 6".oe.-J
l-e I B k Tef'L 't ''.', aLo'e' '!r;e A'
a^61e, o$ Jegv e-cr r'cre o[ -$o-t- o[ -to'"'v
Jft:r- crLo, " dc,fc' tt r7 erenfal e' 'f-'-"'.
a! I Aou'^,.
j".t.o Bx I pe. *" ". {,"7.-"".-.' T'?- ax- b-.,-lrt A. FBd r^ -AgBxlana . 3p ^ 1..r^8, @:-BY("I O*'_O
-tr6rr, o e,: p.
ob' n.V,' "
o@
56.
t""F=rQ
QX
Sx-tg11 --PQ" ll(r- Lo..6a..,rl^-.-FrcrnF
.A e 'ocl c -t() -l) 1oare. = B. tc,^... r rrbp.
itaf3t"r c{ ob{"",ra, = AB = r.s.,..fi2,6i-'r Dh tor.,e -r = pq, = Bo.-.+,e J6l-, r o[ +oux" oAowe JFe, otce-,,ro
D & i o,-'re, te lc,,ea.., tocoe,. &
e Le orgtc ,fi et-t.-t''o-r of
Sli alore- daha 11 vepere.tr:J
ft {o'- o}- ff?- ". {hqrn
J...- {J? tcr.,o = ofporil,- riaeA$oce^F cide
ot'r. t ,r, -,
e1e : 3D -l g
Qv - zs,s.".xB- = z*9.5..-'.
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to^ e = 2g.s
4d,
Bc: J-r-?+i,
5#,0,r'= 4g .+BL
=I'99-16.'t6';= 1{..q{'a :-i.f
* sl..,a+fa-, = flo
5t L. r -ou l>z hc fgttlan ,1 foct ErJ 6a"
Let. P *Q te e4u zzL
Jtse aLcve, r'- {o-..at-Po-
{ r'gr*" *-l t[-oc.ro.
e[ rFe-l = t.s..:.q,ita.
?*oL.--j. .1f a-,
cl 9r l,E",c-o -tt-e-(\ 4p = f).E .o , A6?:16.
1L vag-er.^1,..1 g 1.,..,ob,e
d..o., ?x s- 1,4 / QZIA A,
-!.eq(
!5BU
rf.3. -n.
I xq LCA, zktJU
SL". b3 = ZtALV
cz : 'J--./:,
\
cz -- L.6q'+ .r,.
ol'u
J:=t
ar.5
15,.L __
(3
#% eo" = x11{L.
=) {c = 9:5, Eazl= /.lE \v I[T/ 3
v-3
%l. 4 D'l -l .n.
For bo1 r.Ie"r ol rF..'^? rs = roo r..
-Y' mcrde t.4 tl-iUFo' bX.-h*hF 'b L-?(ct'-?
/ ta't6oa J I
i
ffoLod = 6<"- 3cr'
CD
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le- "r,oJ
z. ty ri--'.lX c-.rf tr', b..fta,%? -+o? F-- 4\"'
Ie .144, kf lt ,fq--.zal eh
Fiht .r'ee t- rnt'gts
ffiL rrLauu P''$o".arlo" S
) l'z''"t o! rL'oe'-'^\0
d'a.., BxI Ac, 'y'D+ eL
3.^ dA6x
-Lo. go' = Bx
*t' '1t. 'og"
'r€ FY!1e.,'h.{ g
to+h Iq!,
<"-- .b
6C.
D
5'4 <I] =
BY=
5)" / gvo
i." ?F,4
'i le,"Ahl o! fo".,.o
he,"gt'f of l'ttt
Ax. A
B* =) _: -_ B* + Bx -_ Bu",r
^B ' )- loo
B)\ ._ XY = 5o- tg.n -- ..D4,.
.,(,?-' 4s" = BYeP
t - 40_ t gD = 4oJ-2.n.,t> -E;
nl $L' e aJ oa s+,,"^4 "l Lqt - 4<tb ,."l (l/(
.A2,
CD
5o "o\ l-,,.o .
tor*ogle o[ abvoFP6n oI ob litr +""n f.oi of1o",,.'
-A^q l" o L(U
P - ao"'
,b -lr,F. of toe"." &,^" *-.t 4
'{o {e'--a+,"o., &
e {. "
<,t f''or
,fFe aLova
1k.". ^a
II
?i-I
I lo-l,n
oer.ere^,teJ ,". fu,_ ,J-
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f'o- +,"A,
5- a +ec_
*o.3o"= og,p, -aaj
.!= ss * B13 Bc
9. a ecp
-L* 6o' ..
itg =
-harirr "b
{aw
c = s-oJt.
!Pg'= qlz =etat Bc E{"l3.
9r =;SD.l3
-+lr'tr
CrJ = 5ox3= iSO.,
E , !-o"r.
t{ts Sr t" toat- -a a^d g. & boaf, 1 .
l^'"f6u.r + -L,!qr.'t -l-our c =rh,.o = _\€.
D fll-o.'ce tu ft.r."., 8,6.. = l0oo.4aV1e + alr vcr Fr"* rb * {-o- B, ar : Joo.
-A-1le $ el,+vatfic., "i A &"- q, F=+dalave ,o.l 4"-..".,of-"* er
'!re {o".- "b *Je*,thr
fo
,u\€ ' e t^
1o" so' -
grB -?- A +aq
o"@
a +eef
ADP. -o{ "&
aa./"3 . !, 13 --- O
*o,-,{9o = 49 + llBq
qS f BB{ : +1G rL
-"F...r." kJo,t Ll,ow.,
= 8e -,4
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:) B,B" = "511'. *',
d= GrB, _ too€l- t Ji't t
x G-t€r
= loo({3-r) -_ sot.r3 -r)L
.l' e ,oql" l- o{ J '%l-
I -hor, tp = E ol G -,) ..,h-lI
-le,"3i.t 4 l.".?ta.'= -dB= 6om.Jnefghr ol "[o-."p f,,c,{ f cb = h.o.,A"2re oh .teg'euPo." $ fop o[ tcr-^g 3o_rt
aop oh bufra,%X < -_ ioo
-*n2le oh -{e3yelrrod ob totlo- ofi to-6 .1or r1op oh turldr^? ,p = ai
il"{ a}ow ,t^ {o.,*alp' 6r" ti regr e1a,..,1s.1 ,%
of f '"6u '" a( Jhou:o
d. ctt r .bx I AG , Dx = AL, cD =a^.
i]^ A eox+orrd = ofr = B(
"{ bx|o.' :d = 6o*cr
DX.,
Ao-hAL
c -- (Ao -h) f: -.'. -O
' +a.F = 4s > +a. Ao"AL
_tr t, 'l)
+etz.'
mz {o,-"
Oo
'l3
= 6oAC
2o.ls.o.:> AC- --@
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{""-Ot@
*l efgt,r
q& s,
"4-gl.
'A.3te
"r al orr*r e J
d 9r Fct-"-
of&hove
$ ' 6 '.'-e
a Agst
I
l6o-r,)G = zoJa
6o-l-, : lo
=2 [ - 4orn .
+efet f o$ la'-p pot F =+a'a\'
D& fd,-r" be F,-r,e"., Ia^p gorFl L*rftd,?< Ac--- zo'[i m
> f{42-<<.'ce LeYt^.12a a l-<-"g6i:t D|1 L&ild.""q '< t&Y Foar-'
= Bx -- 60-+ = 6D- +o = LDd)'
oh .-[r'4xl }'ou--Le, = 'l-r' '-e l-rcs.
ta tu.6 rhi3_r bo opp or?li -rPltr
t. tqY^nat1 156 (]l
ar rt-,oL-co.
=&bok I!h\F l.oLtrev-.-tlg{r+ +'oure :o! Jeg''elrr'o.-' ob ", +.- +"p ob
oleo[ deg.av r'cn .'f -t, *..,- ts-p o[ .tr,!l.t loL41=
-kr yvolra 16a l-
Eetau', rt Ppr = ht+g51_@ .,',tCot.fe.a-ta-E
r e1^, r s.a ^1
c.{ '6^ J-}' ( {oi-.Jir-
lo
pfP.*!-
h
=Aes,E
_(DSrB =fo.a
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l. a ABs)_
+'a.p = aA => Bg, = h -OB, *"^P
Ao@ 9 Bs{+Bs} = h * l,.,
{a^., .;-,.p
r-- F
68. He ighF
ct4 c2 Le
-An3la D I-Aogia "b
' ''s. = h{#-;,1 = tt++=:_@pto^" 1a- p
Dr"r lo-c c- teiur..' ahipr = L,ffa.e - 6o.L.:u). f tranEf . rncfyzl.tb4_ tc,^F
o| tou,x " "46 - fD mt( .
*qx> c-an
tRr' aLowe
{'b*'" o-(
?-., ^ Aec,
**F
cle p't.rr'"oo o$
dep..errfc.r ol,
be'F.'te en Co-t
,i0l-1o-rnali cr-)
-llr o rrro .
e, *. o.-, *og o$ 1oc,.,r.r x = Zo"
q -i.-.- +of -b -{oLo.- F =e6:.
ct ct- .
ft -nf.,"^tul P" fo-.- oh
= oFP.: 4q.dj gL-
to, eci _ !qRt'
Ra- = 5D!2
l^ AAat J- ,.-"-t Lcln r< : ^t3*,,
l-Lo. 3o" . _\g = )E.,c,l . g(.- p( - noG-
Bq = 50€
sorfe
t e-a ..Jg
S =se1 1{
- so/ .3-{ 1 =L{-t, $.r. -t.
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D,1 ta.ce
P & to.,c e
betc'se<n c,aw\ ciq_ = log ^13
,vrE:3
"h ca-1 +yo.y1 loe,;,"n = SoG.^F.o!- ca' 1 *,o.\ {or., uo = qb/J^ .r^k'
6+.' +h,&hF of torc*"
+tefsht ob yatL
-+€h ob etr.rcrhppo
-Ang\e o[ e Lcwa Froco $
Jf, aLs'e datc.
fu -cLot ro
Dtanp AX -L CD
*o= 46- too,tX A = og'
J^ ALXA.
Yef>r.Le^+eJ
9. aca,.
fa.,,6 = cx
", td^ 3cf = CxDe'
= be- cxc*o- p = co *
b6
*oloo't- c, x
bAta,",1r " -- toot a*'=)
Dg.
lootLr = c-)cJ3
cx = 5o (Ji r_r)
o$ t ftr = looJ- EoC.rsr-D
De = roDi-cx .*€
cx {Ji- r) =roo.L,. = \OD .^-___- x !:<rt\A-t ,.fi,
r
J'-,-@ +@
-l","gt"t
.*€ = I oo.n.
Cp =' L,r.o.
o[1 tog o[ -oct *"o^" +rp ofi toc,rc,q= s6.
F? 'b -ocb {*,:.o toro.. o(; +oc-c,
P=+t"'{* "b {t"^.
= r so [3 r Ji) yy!-^
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66. 4+e&+ "$ J.!ht '.L,o,re 4 . r5o n,rE.
"le I {,+ I, ta +*o -,L&l a3p'. oac hrD^3 €a.h o+hc''
-/roq\e rf depxtur"oo "b ",
1= 3D"
- 1.(
.rcprere-ha.{
J ,t *". drt -t houol'Gc {o'-., pb
r. n t&9_
ta'.e - aet|q
ron 4K"= !!qBg"
R! > I (ona
66 ' **
".iil.,*+1 e.qh I
-,\.€\e r:k
-Ajle rb
IF4 o,bcn't
1tq *'. at
.C. a Ata
21,{Bc7
-la,. a = 4G&cr
t&i 30" - tSo;;
')\r : l9oJt nt.
of tou:e.r = AB: 8.6.
"b Flag rr.r$f gc- _ r [, ,.ys.
clu".ft"o. ub- +"t "b
eLv-rf-.- $ taa.6daira S
"ep".-iu_.,taJ
6F=
= 5...
"r,tI
.g1e
11nqle of clcprer.rioo -fr ", F = 4eD &Fo-.. te Ft',< co -rl"1og
.-[F, oL,q-,e "lata fo
g I 3' = e! - B-r, = lso tJe -1)
",^tTD& fo..t., !'eF.o<<n _rU, ft_r = l\.o1.ft-*i )
(ta?(LaIh
tr.ffF-bbE{*
a( = 6o9
F' 45".
l'}.;1
!
't'-
e= +e
6
at,RD Sharma Class 10 Solutions Applications of Trigonometry
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Page 64
5. a'151 ,
.|,e,!t r
61 . +l ea'flht
kF 7oP^b
p",0. t o
3'"*+" "i, F
] 01ur? ed tu
Ifu aLpv"
O-l (hocoo.
C. aAsL)
f^ a 4e,
...arffpty- O*@
tana - ,{c.Ap
tarr 6d= &"e. =AI)
Ltg
"h
q-
r": = trgrh r-r. 9.& "+ h = scJ-ett = 9,r p.1g > = 3.LrMh -
-t Ia3r|" bh :3.6-cMt.
pYov. *{'ar h = 6..,.h .
daha. & v1'ertntz.l ,l- 6o {e'"- "}- (,b""
la^x= ABk.
la^"r = b1
b"p= 4s = h t ,3'n.--leD1
*"^ (qo- /) = l,3
o\ loacr ,+B = 'd'.,.tt.c LL 4-k $.o"" B , -,{.gte + e tevatrL i' <
Lr I '.h $o.o. B, -&o2ra "i et".rot3o. t p.a'r? to'n7le-'.,l..-t4 . ,(+F - ?o" :> F = 1b"-d.
h= qthtc_@l^,<h= 1fc.^,c x g coFa
= 36 .Ctao<. cof*)hz = 3sn= '/:6 = 6-6.
4 tou:."r = 4.."|;'.
RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in
RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in
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Page 65
.68- +tr-t!1t.'r
l-el q* q
4..'la ol0l/-4.nle r[
.i.'....hf aLoe
oL.thqr4,g 4 Aa{
-:L^
"b l,frlf, Lo-.r" ,+s ='1,'."rrt;,,.te ohfu d&to,-re te l.,:ea., {hft{ !,1_deg".,<,%r, "l {, &. sr! ? zer,,^.
c{eg"csr$" oi r_, 16 = +{.dat-o ft r3'ae"lzd f^ {o* ob e.,-"
*o",e = ABI _:-
r{Luan 15o = h
Bsr-
--.=h-_{DA 433, *or, < - l\8
g!rtz1^ Scf = 4
AgL
= 2 oo [Jg+,; '=
Rs+ = h(i .._-@
Bs, -es_. = ;,6;i_,aoo = h(e_r_)
|r = 20." ,l \j 3-t Ifci Giih = too (t..r31 ,,; . 2 i j.2 Mh.
+e.fgut- Dt- .tfgt l L'o.ue = ,t3, dk.
t oo (J"s r ,J .ra L
RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in
RD Sharma Class 10 Solutions Applications of Trigonometry www.LearnCBSE.in
Learn
CBSE.in
Le
arnCBSE.in