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 of elevation on the ground.
In ∆EDC
tan 60° = 
h = √3
--------(1)
In ∆ABC
tan 30° = 
√3h = 80-
----------(2)
On substituting value of h from eqn.(1) in eqn. (2)
√3
3
4
= 80
On substituting value of 
in eqn. (1)
√3h = 80-20⇒ 60
h = 
⇒ 
⇒ 
h = 20√3 m.
Therefore height of poles is 20√3 m. and distances of the points from one pole is 20 m. and from other pole is 80-20 = 60 m.
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