The angle of elevation of a tower from a point on the same level as the foot of the tower is 30°. On advancing 150 meters towards the foot of the tower, the angle of elevation of the tower becomes 60°. Show that the height of the tower is 129.9 metres (Use ).

Question

The angle of elevation of a tower from a point on the same level as the foot of the tower is 30&#xB0;. On advancing 150 meters towards the foot of the tower, the angle of elevation of the tower becomes 60&#xB0;. Show that the height of the tower is 129.9 metres (Use ).

Philoid · Accepted Answer

Let the height of the tower = h (m)

In ∆ABC,

tan 30° =

=

√3h = 150+

-------- (1)

In ∆ABD,

tan 60° =

√3 = ⇒ h = √3

-------(2)

on substituting value of x from eqn.(2)i eqn.(1)

h-3h = -150

2h = 150√3

h = ⇒ 75

h= 129.9 m.

Hence height of tower is 129.9 m.