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PQ is a vertical tower, P is the foot, Q the top of the tower, A, B, C are three points in the horizontal plane through P. The angles of elevation of Q from A, B, C are equal and each is equal to θ. The sides of the triangle ABC are a, b, c and the area of the triangle ABC is ∆. The height of the tower is

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none of these

(abc) cot θ /4∆

(abc) tan θ /4∆

answer is A.

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Detailed Solution

AQ = BQ = CQ = h cot θ

∴ Q is circumcentre of ΔABC $\begin{array}{l} ∴ A Q = B Q = C Q = R = \frac{a b c}{4 Δ} \\ ∴ h = \frac{a b c \tan θ}{4 Δ} \end{array}$

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