If $ P Q $ be a vertical tower subtending angles $ \alpha, \beta $ and $ \gamma $ at the points $ A, B $ and $ C $, respectively on the line in the horizontal plane through the foot $ Q $ of tower and on the same side of it, then $ B C \cot \alpha-C A \cot \beta+A B \cot \gamma $ is equal to

Question

If $ P Q $ be a vertical tower subtending angles $ \alpha, \beta $ and $ \gamma $ at the points $ A, B $ and $ C $, respectively on the line in the horizontal plane through the foot $ Q $ of tower and on the same side of it, then $ B C \cot \alpha-C A \cot \beta+A B \cot \gamma $ is equal to, $ 0 $, $ 1 $, $ 2 $, None of these

MARKS App · Accepted Answer

Let h be the height of the tower, then h = A Q tan α = B Q tan β = C Q tan γ ⇒ B C = B Q - C Q = h cot β - cot γ , C A = h cot α - cot γ and A B = h cot α - cot β Now, B C cot α - C A cot β + A B cot γ = h cot α cot β - cot γ - cot β cot α - cot γ + cot γ cot α - cot β = 0

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