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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.

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34 m

34.64 m

18 m

30 m

answer is A.

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Detailed Solution

Given that, two poles of equal heights standing opposite each other on either side of the 80 m wide road.
The angle of elevation from a point on the road to the top of the poles are

60 °

and

30 °

.
Draw the diagram depicting the situation.
Question Image

Let

d 1

be the distance between point and left pole.
Determining the distance

d 1

d 1 = h tan 60 ° ⇒ d 1 = h 3

Let

d 2

be the distance between point and right pole.
Determining the distance

d 2

d 2 = h tan 30 ° ⇒ d 2 = h 3

Determine the height of the poles.

h 3 + h 3 = 80 ⇒ h + 3 h = 803 ⇒ 4 h = 803 ⇒ h = 203 ⇒ h = 34.64

Hence, height of poles: 34.64 m.
Hence the correct option is 1.

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