29 The points P, Q, and B lie in a horizontal plane. From P, which is due west of B, the angle of elevation of the top of a tower AB of height h meters is 42°. From Q, which is on a bearing of 196° from the tower, the angle of elevation of the top of the tower is 35°. The distance PQ is 200 metres. a Explain why

Trigonometry (MindTap Course List)
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Chapter7: Triangles
Section7.1: The Law Of Sines
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I need help with part a and b.

29 The points P, Q, and B lie in a horizontal plane. From P, which is due west of B, the angle of elevation of
the top of a tower AB of height h meters is 42°. From Q, which is on a bearing of 196° from the tower, the
angle of elevation of the top of the tower is 35°. The distance PQ is 200 metres.
a Explain why ZPBQ = 74º.
b
200²
cot² 42° + cot²35° - 2cot 35° cot 42° cos 74°
c Hence find the height of the tower, correct to the nearest metre.
Show that h²
=
P
200 m
42°
Q
35⁰
A
B
Transcribed Image Text:29 The points P, Q, and B lie in a horizontal plane. From P, which is due west of B, the angle of elevation of the top of a tower AB of height h meters is 42°. From Q, which is on a bearing of 196° from the tower, the angle of elevation of the top of the tower is 35°. The distance PQ is 200 metres. a Explain why ZPBQ = 74º. b 200² cot² 42° + cot²35° - 2cot 35° cot 42° cos 74° c Hence find the height of the tower, correct to the nearest metre. Show that h² = P 200 m 42° Q 35⁰ A B
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