Multiple choice

The angle of depression of two points P and Q on the ground on either side of pole, from top of the poles are 60° and 30° respectively. Then find the height (in meter) of the pole if the distance between point P and Q is 84√3m?

  1. 60

  2. 52.5

  3. 73.5

  4. 63
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D Correct answer
Explanation

Let the pole height be h. For point P (angle 60°): tan(60°) = h/x₁, so x₁ = h/√3. For point Q (angle 30°): tan(30°) = h/x₂, so x₂ = h√3. Total distance PQ = x₁ + x₂ = h/√3 + h√3 = 4h/√3. Given PQ = 84√3, so 4h/√3 = 84√3, giving h = (84√3 × √3)/4 = 84 × 3/4 = 63m.

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