Home
Class 10
MATHS
Two poles of equal heights are standing...

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 `60o`and `30o`, respectively. Find the hei

Text Solution

Verified by Experts

Let AB and CD be two poles of equal height 'h', standing on either side of a road of width 80 m.
At point E, given that
`angle CED=60^(@)" and " angle AEB=30^(@)`
Let `DE=x`
`:. BE=80-x`
In `DeltaCDE`,
`tan60^(@)=(CD)/(DE) rArr sqrt3=h/x rArr h=xsqrt3 ...(1)`
In `DeltaABE`,
`tan30^(@)=(AB)/(BE) rArr1/sqrt3=h/(80-x)rArr1/sqrt3=(xsqrt3)/(80-x)" [from(1)]"`
`rArr 3x=80-x rArr 4x=80 rArr x=20`
`:. 80-x=80-20=60" and "h=20sqrt3`
`:. " Height of each poles " 20sqrt3m`
Distance of point E from two poles =20 m and 60 m
Promotional Banner

Topper's Solved these Questions

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|32 Videos

  • SOME APPLICATIONS OF TRIGONOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (short Answer Questions)|5 Videos

  • REAL NUMBERS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|5 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|4 Videos

Similar Questions

Explore conceptually related problems

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.

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.

Two pillars of equal heights stand on either side of a roadway, which is 150 m wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60^(@) and 30^(@) . Find the height of the pillars and the position of the point

Two men on either side of the cliff 80m high observes the angles of elevation of the top of the cliff to be 30o and 60o respectively. Find the distance between the two men.

A T.V. Tower stands vertically on a bank of a river. From a point on the other bank directly opposite to the tower, the angle of elevation of the top of the tower is 60 degrees. From a point 20m away this point on the same bank, the angle of elevation of the top of the tower is 30o . Find the height of the tower and the width of the river.

There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30o and 60o respectively. Find the width of the river and the height of the other temple.

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60^0a n d30^0 respectively. Find the height of the tower and the flag pole mounted on it.

From te top of a tower , 60 meters high, the angles of depression of the top and bottom of a pole are alpha and beta respectively .Find the height of the pole.

Two pillars of equal height and on either side of a road, which is 100m wide. The angles of elevation of the top of the pillars are 60^@ and 30^@ at a point on the road between the pillars. Find the position of the point between the pillars and the height of each pillar.

From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45o and 60o respectively. Find the height of the pole.