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`

Explanation

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)`

...