## Finding the Height of a Hill

A surveyor is trying to find the height of a hill. He takes a sight on the top of the hill and finds that the angle of elevation is 40°. He moves a distance of 150 metres on level ground directly away from the hill and takes a second sight. From this point, the angle of elevation is 22°. The task is to find the height of the hill.

What is the height of the hill?
height ≈ 60.60 m
Explanation:
The surveyor is trying to find the height of the hill. He takes a sight on the top of the hill and finds the angle of elevation is 40°. The distance from the hill where he measured the angle of elevation of 40° is not known.
Now he moves 150 m on level ground directly away from the hill and takes a second sight from this point and measures the angle of elevation as 22°. This illustration forms a right angle triangle. The opposite side of the triangle is the height of the hill. The adjacent side of the triangle which is 150 m is the distance on level ground directly away from the hill.
Using tangential ratio,
tan 22° = opposite/adjacent
tan 22° = h/150
h = 150 × tan 22°
h = 150 × 0.40402622583
h = 60.6039338753
height ≈ 60.60 m