● 3 16.1–16.2 Pythagoras’ Theorem 337A 1 Find the length of the hypotenuse in each triangle, correct to 3 significant figures. a b .................................................................. .................................................................. c d .................................................................. .................................................................. 2 An extending ladder is placed 9.5 m from the base of a building. Calculate the length of the ladder when it reaches these heights on the building wall. a 4.7 m .................................................................. b 7.4 m ................................................................. c 12.9 m .................................................................. d 17 m .................................................................. Guided practice worksheet (hypotenuse) 2 = (short side) 2 + (other short side) 2 a 2 = 14 2 + 9 2 = 196 + 81 = 277 a = √277 = 16.64331698 (write more than 3 significant figures from your calculator…) a = 16.6 cm (3 s.f.) (… then round your answer to the required degree of accuracy) 14 cm 9 cm a 7.5 cm 5.3 cm 25 mm 20 mm 7 cm 3 cm 9.5 m 1 m 1 m C Questions are targeted at the grades indicated
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�3 16.1–16.2 Pythagoras’ Theorem
337A
1 Find the length of the hypotenuse in each triangle, correct to 3 signi� cant � gures.
2 An extending ladder is placed 9.5 m from the base of a building.
Calculate the length of the ladder when it reaches these heights on the building wall.
a 4.7 m .................................................................. b 7.4 m .................................................................
c 12.9 m .................................................................. d 17 m ..................................................................
Guided practice worksheet
(hypotenuse)2 = (short side)2 + (other short side)2
a2 = 142 + 92 = 196 + 81 = 277a = √277 = 16.64331698 (write more than 3 signi� cant � gures from your calculator…)a = 16.6 cm (3 s.f.) (… then round your answer to the required degree of accuracy)
14 cm
9 cm
a
7.5 cm
5.3 cm
25 mm
20 mm
7 cm
3 cm7.5 cm
5.3 cm
1 m
1 m
25 mm
20 mm
9.5 m
1 m
1 m
C
Questions are targeted at the grades indicated
�3 16.1–16.2 Pythagoras’ Theorem
337B
Guided practice worksheet
3 Find the length of the side marked with a letter, correct to 3 signi� cant � gures.
�3 16.4–16.5 Using trigonometry in right-angled triangles
341A
Guided practice worksheet
1 Use your calculator to � nd the value of the following, correct to 4 decimal places, where necessary.
a sin 30° ............................................................................. b tan 10° .............................................................................
c cos 90° ............................................................................. d sin 28° .............................................................................
e cos 1° ............................................................................. f tan 88.2° .............................................................................
2 Use your calculator to � nd the value of x, correct to 1 decimal place, where necessary.
a tan x = 1 ............................................................................. b sin x = 0.7 .............................................................................
c cos x = 0.25 ............................................................................. d sin x = 0 .............................................................................
e tan x = 3.1 ............................................................................. f cos x = 0.05 .............................................................................
g sin x = 0.216 ............................................................................. h tan x = 33
The two sides we know are Adjacent (4.2 cm) and AdjHypotenuse (6.3 cm), so use cos x = ––– Hyp 4.2cos x = ––– = 0.666… 6.3x = 48.18968511 ... (press [sin–1] to � nd angle x)x = 48.2° (1 d.p.)
x
4.2 cm
6.3 cm
a
7 mm
9 mm
b2.5 cm
1 cm
c
100 m75 mm
d
0.6 cm 0.7 cm
a
7 mm
9 mm
b2.5 cm
1 cm
c
100 m75 mm
d
0.6 cm 0.7 cm
a
7 mm
9 mm
b2.5 cm
1 cm
c
100 m75 mm
d
0.6 cm 0.7 cm
a
7 mm
9 mm
b2.5 cm
1 cm
c
100 m75 mm
d
0.6 cm 0.7 cm
B
Questions are targeted at the grades indicated
C
�3 16.4–16.5 Using trigonometry in right-angled triangles
341B
Guided practice worksheet
4 Find the length of each side marked with a letter, correct to 3 signi� cant � gures.
x is the side Opposite the angle 40° and 15 mm is the OppAdjacent side, so use tan x = ––– Adj xtan 40° = ––– 15 x0.839099631... = ––– 1515 × 0.839099631 ... = x (multiply both sides by 15)x = 12.6 cm (3 s.f.)
15 mm
x
40°
18 cm
a
30°
4.2 m
b
50°
100 mm
c
d
26°
0.25 m
81°
18 cm
a
30°
4.2 m
b
50°
100 mm
c
d
26°
0.25 m
81°
18 cm
a
30°
4.2 m
b
50°
100 mm
c
d
26°
0.25 m
81°
18 cm
a
30°
4.2 m
b
50°
100 mm
c
d
26°
0.25 m
81°
B
�3 16.4–16.5 Using trigonometry in right-angled triangles
341C
Guided practice worksheet
5 Trevor drove from Cardiff to Leeds and then � ew due north from Leeds to Newcastle.Use the dotted right-angled triangles to answer the following questions.