# Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point between them on the road the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.

Let AB and ED are two poles of equal height.

Let C be the point between the poles on the ground.

Since poles are vertical to the ground.
In a right-angled triangle, we know,

In ∆EDC

tan 60° =

h = √3 --------(1)

In ∆ABC

tan 30° =

√3h = 80-x----------(2)

On substituting value of h from eqn.(1) in eqn. (2)

√3 × √3x = 80 - x

⇒ 3x = 80 - x

⇒ 4x = 80

⇒ x = 20 m

On substituting value of in eqn. (1)

h = 20√3
Distance of C from pole ED = 20 m
Distance of C from pole AB = 80 - 20
= 60 m

Therefore the height of the poles is 20√3 m. and distances of the points from one pole is 20 m and from other pole is 60 m.

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