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Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as 45 o and 30 o respectively. If the height of the tower is 40 m , then the distance between the men is

Options

  1. A40   m
  2. B40 3 m
  3. C68 . 28   m
  4. D109 . 28 m

Correct answer

D. 109 . 28 m

Step-by-step solution

From Δ O 1   A B ,   tan ⁡ 45 o = 40 x   ⇒     x = 40   m From Δ O 2 A B ,   cot ⁡ 30 o = y 40 ⇒ y = 40 3   m Distance between the men = 40 + 40 3   = 109.28   m .

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