Question

A tree x m high the angle of elevation of its top from a point P on the ground is 23. from another point Q, 10 m from P and in line with P and the foot of the tree, the angle of elevation is 32. Find x.

Answer 1

Answer on Question #48997 – Math – Trigonometry

A tree x m high the angle of elevation of its top from a point P on the ground is 23. from another point Q, 10 m from P and in line with P and the foot of the tree, the angle of elevation is 32. Find x.

Solution

As we get 2 rectangular triangles ABQ and APB with right angle B, in which AB = x,

BQ = x/tg32°, BP = x/tg23°, PQ = 10, and as BP = BQ + PQ, then:

x/tg23° = x/tg32° + 10

x(1/tg23° - 1/tg32°) = 10

x = 10/(1/tg23° - 1/tg32°) = 13.24 m

So, the height of the tree is 13.24 m.

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