A flag pole on the top of a mall building is 75 m high. The height of the mall building is 325 m. To an observer at height of 400 m, the mall building and the pole subtend an equal angle Ө. If the horizontal distance of the observer from the pole is x, what is the value of x?
Explanation:
Consider the layout of the mall, flag pole and oberver as shown below. Let the horizontal distance from the oberver to the pole be d m. Considering pole: tan θ = 75/d ... (i) Considering mall building: tan 2θ = 400/d ... (ii) ∴ (2tanθ) / (1 − tan2θ) = 400/d ∴ 2(75/d) = (400/d) × [1 − (75/d)2] ∴ 1 − (5625/d2) = 3/8 ∴ (5625/d2) = 5/8 ∴ d2 = 5625 × (8/5) = 9000 ∴ d = 900 × 10 = 30√10 m Hence, option (b).
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