Question

The angle of elevation of the top of a tower standing on a horizontal plane from a point C is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is
A.d/cotα+cotβB.d/cotα-cotβC.d/tanβ-tanαD.d/tanβ+tanα

Answer 1

The angle of elevation of the top of the tower from point C is given as α.

The angle of elevation of the top of the tower from point B is given as β.

Let distance from C to the base of the tower be x.

Distance between B and C is given as d.

1. Cotα = x/h  and  Cotβ = (x-d)/h
2. Therefore, Cotβ = (x/h) - (d/h)
3. Cotβ = Cotα - d/h
4. d/h = Cotα - Cotβ
5. h = d/(Cotα - Cotβ)

Hence, answer is Part C ie d/(Cotα - Cotβ)