The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α .After walking a distance d towards the foot of the tower the angle of elevation is found to be β . Find the height of the tower. (Ans: d/cot α - cot β)

Ans: Let BC = x

tan β =  AB/CB

tan β = h/x

x = h/tan β

x = h cot β     ---------(1)

tan α = AB/DC + CB

tan α = h /d + x

d + x = h/tan α  = hcotα

x = h cot  α - d ----------(2)

from 1 and 2

h cot β =  h cot  α - d

h (cot α - cot β ) = d

h = d /cot α - cot β