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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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