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Question

A tower subtends angles θ, 2θ and 3θ at three points A,B,C respectively lying on a horizontal line through the foot of tower. Then the ratio ABBC equals

A
sin3θsinθ
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B
sinθsin3θ
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C
cos3θcosθ
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D
tanθtan3θ
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Solution

The correct option is A sin3θsinθ

tan3θ=hQCQC=hcot3θ
Similarly,
QB=hcot2θQA=hcotθ

ABBC=QAQBQBQCABBC=cotθcot2θcot2θcot3θABBC=sin3θsinθ

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