(Q9) Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet wide. From a point between them on the road, the angles of elevation of the top of the poles are 60^o and 30^o respectively. Find the height of the poles and the distances of the point from the poles.

Solution :

Width of the road = 120 f.

Angle of elevation of the top of the 1st tower = 60°.

Angle of elevation of the top of the 2 tower = 30°.

Let the distance of the point from the 1st pole = x.

Then the distance of the point from the 2nd pole = 120 - x.

and height of each pole = h say.

From the figure

h = √ x ....(1)

from (1) and (2)

√.√ x = - x

x = - x

x + x =

x =

x = ft

Now h = √ x = √× = 1.732 x = .960 feet

∴ Distances of the poles = ft. and 120 - fts = ft.

Height of each pole = .96 ft.