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The angle of elevation of the top of a t...

The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is `sqrt(st)`.

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Let BC be a tower of height 'h'. Let `AC=s" and "DC=t`. From points A and D, the angle of elevation of top B of the tower are complementary.
Let `angleBAC=theta`
`:. angleBDC=90^(@)-theta`
In `DeltaBAC`
`tantheta=(BC)/(AC)=h/s …(1)`
In `DeltaBDC`
`tan(90^(@)-theta)=(BC)/(CD)rArrcottheta=h/t`
`rArr 1/(tantheta)=h/trArrs/h=h/t" [from(1)]`
`rArr h^(2)=strArrh=sqrt(st)`
`:. " height of the tower "=sqrt(st)`
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