1.

PQ is a vertical tower having P as the foot. A,B,Care three points in the horizontal plane through P. The angles of elevationof 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 ABCis ``. Then prove that the height of the tower is (abc) `tantheta/(4)dot`

Answer» Let `h` is the height of the tower.
Then,
`AP = BP = CP = hcot theta`
Please refer to video to see the diagram.
Here, `P` is the circumcenter of `Delta APC`.
`:. AP = BP = CP = R = (abc)/(4Delta)`
`=>(abc)/(4Delta) = hcottheta`
`=>h = 1/cottheta(abc)/(4Delta)`
`=>h = (abc)tantheta/(4Delta).`
So, height of the tower is ` (abc)tantheta/(4Delta).`


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