Home
Class 12
MATHS
From te top of a tower , 60 meters high,...

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.

Text Solution

Verified by Experts

Let AE be the tower ,CD be the pole and d be the distance between the tower and the pole .Also let h be the height of the pole.

In triangle ABC d=(60 h ) cot `alpha`
In triangle AED , d = 60 cot `beta`
`therefore 60 cot beta =(60 -h ) cot alpha`
`rArr h=(60 (cot alpha - cot beta )/(cot alpha))`
Promotional Banner

Topper's Solved these Questions

  • HIGHT AND DISTANCE

    CENGAGE|Exercise Exercise|18 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise|22 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

Similar Questions

Explore conceptually related problems

From the top of the tower 60 m high the angles of depression of the top and bottom of a vertical lamp post are observed to be 38^(@) and 60^(@) respectively. Find the height of the lamp post. (tan38^(@)=0.7813, sqrt(3)=1.732)

From the top of tree of height 13m the angle of elevation and depression of the top and bottom of another tree are 45^(@) and 30^(@) respectively. Find the height of the seconds tree. (sqrt(3)=1.732) .

From a point on the roof of a house, 11m high, it is observed that the angle of depression of the top and foot of a lamp post are 30^@ and 60^@ respectively. What is the height of the lamp post?

Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet 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.

A ship of height 24 m is sighted from a lighthouse. From the top of the lighthouse the angle of depression to the top of the mast and base of the ship is 30^@ and 45^@ respectively. How far is the ship from the lighthouse ? ( sqrt3 = 1.73 )

From the bottom of a pole of height h, the angle of elevation of the top of a tower is alpha . The pole subtends an angle beta at the top of the tower. find the height of the tower.