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    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.
    A 20√3 ft Correct Answer Incorrect Answer
    B 16√3 ft Correct Answer Incorrect Answer
    C (48√2 + 4) ft Correct Answer Incorrect Answer
    D (20√3 + 4) ft Correct Answer Incorrect Answer

    Solution

    Image

    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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