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      Question

      From a point on the ground, the angle of elevation of

      the top of a tower is 45°. On walking 20 m towards the tower, the angle of elevation becomes 60°. Find the height of the tower.
      A 17(3 + √3) m Correct Answer Incorrect Answer
      B 10(5 + √3) m Correct Answer Incorrect Answer
      C 10(3 + √3) m Correct Answer Incorrect Answer
      D 10(2 + √2) m Correct Answer Incorrect Answer

      Solution

      Let initial distance from tower = x m, height = h m. tan 45° = h / x ⇒ 1 = h/x ⇒ h = x After moving 20 m towards tower, distance = x − 20: tan 60° = h / (x − 20) ⇒ √3 = h/(x − 20) Since h = x: √3 = x / (x − 20) √3(x − 20) = x √3 x − 20√3 = x (√3 − 1)x = 20√3 x = 20√3 / (√3 − 1) Rationalize: x = 20√3(√3 + 1) / (3 − 1) = 10√3(√3 + 1) = 10(3 + √3) Height h = x = 10(3 + √3) m.

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