Q. 104.1( 333 Votes )

# 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

Answer :

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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PREVIOUSThe angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the buildingNEXTA TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal

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