at a point on a level plane, a tower subtends an angle alpha and a man, a meters tall standing on its top, subtends an angle beta. prove that the height of the tower is acot(alpha+beta)/cot alpha - cot (alpha+beta)

Here, the height of tower is found as:

Let AD be the tower and DC denotes the man of height 'a' m standing on the top of tower. Let O be a point on the plane containing the foot of the tower such that angle of elevation of the man and the tower at point O are A and B respectively.

Let OA = x metres

Let the height of tower, AD be y meters and DC = a metres.

In ∆OAD we have

In ∆OAC we have

Now equating (1) and (2), we get

Hence, the height of tower .