The angles of elevation of the top of a tower from two points at distances `a` and `b` metres from the base and in the same straight line with it are complementary. Prove that the height of the tower is `sqrt(a b)` metres.

Explanation

Given,
the angle of elevation of the top of the tower from two points P & Q is at a distance of a & b.

Also given, to prove that the tower

`height =sqrt{a b}`

(becauseright. complementary angle `=(90^{circ}-theta))`

From triangle {ABP}


`tan theta=frac{{AB}}{{BP}}=frac{{AB}}{{a}} ldots ldots(1)`

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