# Two poles of equal heights are standing opposite 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 DE be the two poles, and C be the point of observation.
Given,
width of road, BD =  80 m
Angle of elevation to AB, ∠ACB = 30°
Angle of elevation to DE, ∠ ECD = 60°
To find: Height of buildings AB and DE.

In Δ ACB

In Δ EDC:

We know that AB = ED as the poles are of same height.

Hence, from (i) and (ii),

cross multiplying, we get

Now, using the value of BC in (i),

AB = 20√3 m
Now from triangle EDC,

Therefore,
Height of Pole = 20√3 m
Distances of poles from observing point = 60 m and 20 m

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