Surveyor Calculating Height of a Hill

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
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