Question
From the top of a tower, the angle of depression to the top
of a man's head is 60°. The man is 4 feet tall and is standing 20 feet away from the base of the tower. Determine the total height of the tower.Solution
Let CE = height of the tower and AB is the height of the man.
Let ED = 'x' ft
So, height of tower = (x + 4) ft
Given, AD = 20 ft
In right triangle EDA,
tan60 o = (ED/DA)
Or, tan 60 o = (x/20)
Or, √3 = (x/20)
So, x = 20√3
So, height of the tower = (20√3 + 4) ft.
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