SECTION 8-6 SECTION 8-6 Law of Sines Law of Sines Jim Smith JCHS Jim Smith JCHS 3108.4.49 3108.4.49 Use the Law of Sines to find missing side lengths and/or Use the Law of Sines to find missing side lengths and/or angle measures in non-right triangles angle measures in non-right triangles
16
Embed
SECTION 8-6 Law of Sines Jim Smith JCHS 3108.4.49 Use the Law of Sines to find missing side lengths and/or angle measures in non-right triangles.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
SECTION 8-6SECTION 8-6Law of SinesLaw of Sines
Jim Smith JCHSJim Smith JCHS
3108.4.493108.4.49Use the Law of Sines to find missing side lengths and/or Use the Law of Sines to find missing side lengths and/or angle measures in non-right trianglesangle measures in non-right triangles
A Car Runs Into A Telephone A Car Runs Into A Telephone Pole AndPole And
Knocks It Off Perpendicular To Knocks It Off Perpendicular To The Ground By 9°. If The PoleThe Ground By 9°. If The Pole’’s s
ShadowShadowIs 57 Feet Long And The Angle Is 57 Feet Long And The Angle
Of Of Elevation From The Ground To Elevation From The Ground To
The Top The Top Of The Pole Is 48°, How Can We Of The Pole Is 48°, How Can We
Find Find The Height Of The Pole?The Height Of The Pole?
Let a = 7 cm, ∠B = 45°, and ∠C = 75°.
Is there a unique triangle with the given angle and side measures? Why? How might you determine the measures of the missing angle and sides?
What method did we use to findthe height of a tree?
What measures did we need tofind the height of a tree or a pole?
If the pole is leaning at an angle,why can’t we use sin, cos, or tangent?
The Law Of Sines Allows Us To WorkThe Law Of Sines Allows Us To Work
With Triangles Other Than RightWith Triangles Other Than Right
Triangles. Triangles.
In A Triangle, The Ratio In A Triangle, The Ratio
Of The Sine Of An Angle And Of The Sine Of An Angle And
The Length Of The Side The Length Of The Side
OppositeOpposite
That Angle Are The Same That Angle Are The Same
For For
Each Pair Of Angles And Each Pair Of Angles And
Sides.Sides.
They are ___________________They are ___________________
Proportional
AA
BB
CC
cc aa
bb
c
C
b
B
a
A sinsinsin
Students will be able to writethe law of Sines formula
Students will be ableStudents will be ableto find the missing side ofto find the missing side ofa non-right trianglea non-right triangle
AA
BB CC
85°85°
70°70°
XX
1515
X
70sin
15
85sin
)70(sin15)(85sin X
85sin
)70(sin15
85sin
)(85sin
X
85sin
)70(sin15X
15.14X
AAS
ACT FORM
X
70sin
15
85sin
)70(sin15)(85sin X
85sin
)70(sin15
85sin
)(85sin
X
85sin
)70(sin15X
15.14X
X
9396.
15
9961.
)9396(.159961. X
9961.
10.14
9961.
9961.
X
15.14X
“Another way to skin a cat”
Back To The Car AndBack To The Car And Telephone PoleTelephone Pole
A Car Runs Into A Telephone A Car Runs Into A Telephone Pole AndPole And
Knocks It Off Perpendicular To Knocks It Off Perpendicular To The Ground By 9°. If The PoleThe Ground By 9°. If The Pole’’s s
ShadowShadowIs 57 Feet Long And The Angle Is 57 Feet Long And The Angle
Of Of Elevation From The Ground To Elevation From The Ground To
The Top The Top Of The Pole Is 48°, How Can We Of The Pole Is 48°, How Can We
Find Find The Height Of The Pole?The Height Of The Pole?
9°9°
575748°48°
Do you know how to solve it now?Do you know how to solve it now?
9°9°
48°48°5757AA
BB
CC
xx
990 BCA
81°81°
51°51°
57
51sin48sin
x
48sin57)(51sin x
51sin
48sin57x
51.54x
LetLet’’s find an angle…s find an angle…Look at a right triangle fromLook at a right triangle from
last week first …last week first …
10102222
22
10 xofsin
00.27x
xx
55 33
xx 50°50°
5
50sin
3
sinx
)50(sin3)(sin5 x
5
)50(sin3sin x
36.27x
Students will be ableStudents will be ableto find the missing angle ofto find the missing angle ofa non-right trianglea non-right triangle