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The angles of elevation of the top of a tower from two points at a distance of 4m

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The angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6m.

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Let the height of tower, PQ = h m.

 AQ = 4 m, BQ = 9 m. 

∠PAQ = θ ∠PBQ = 90 – θ

From eqn. (i) and eqn. (ii),

∴ h2 = 36 

∴ h = 6 m 

∴ Height of tower, h = 6 m.

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