Question

An Engineer standing on the ground level at certain distance from the towner observed that angle of elevation is 60°. By moving further distance of 30 m away from his original position he observed that the angle of elevation is 30° . Help him to find the height of the towner.

Answer 1

height of tower be h
initial distance from the foot to engineer is x
tan60° = h/x
⇒h = x√3___(1)
also, tan30° =h/(x+30)
⇒h = (x+30)/√3____(2)
equating (1) and (2)
(x+30)/√3 = x√3
⇒x +30 = 3x
⇒2x = 30
⇒x =15 m
so height, h = 15√3 m