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