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PQ is a vertical tower having P as the f...

PQ is a vertical tower having P as the foot. 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 `theta` . The sides of the triangle ABC are a,b,c, and area of the triangle ABC is `triangle` . Then prove that the height of the tower is (abc) `tantheta/(4 'triangle' dot`

Text Solution

Verified by Experts

Let the height of the tower PQ be h.

AP = BP =CP =`h cot theta`
Therefore , P is the circumcentre of `DeltaABC`
`therefore AP=BP =CP = R = (abc)/(4Delta)`
`therefore h= (abc)/(4Delta)tantheta`
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