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Two poles are x m apart and the height of one is double of the other. If from the mid – point between the two, an observer finds an elevation of their tops to be complementary, then what will be the height of the shorter pole?

Two poles are x m apart and the height of one is double of the other. If from the mid – point between the two, an observer finds an elevation of their tops to be complementary, then what will be the height of the shorter pole? Correct Answer x / 2√2 m

Let the height of shorter pole = h m, longer pole = 2h m. Let the angle of elevation of shorter pole = y degree, then for longer pole = 90 – y degree. ➩ tan y = height / base distance ➩ tan y = h / (x / 2) ➩ tan y = 2h / x Also, ➩ cot (90 – y) = base distance / height ➩ cot (90 – y) = (x / 2) / 2h ➩ cot (90 – y) = x / 4h As the angles are complementary: ➩ 2h / x = x / 4h ➩ 8h2 = x2 ➩ h = x / 2√2 m

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