The angle of elevation of the top of a tower from a point` A` due south of the tower is `alpha` and from `B` due east of tower is `beta`. If `AB=d`, show that the height of the tower is `d/sqrt(cot^2 alpha+ cot^2 beta)`.

Explanation

Let O P be the tower and let A and B be two points due south and east respectively of the tower such that


`angle {OAP}=alpha`


and `angle O B P=beta.`

Let {OP}={h}

In triangle O A P, we have

`tan alpha=frac{h}{O Lambda}`

...