Advertisements
Advertisements
प्रश्न
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 45° and 60° respectively. Find the height of the pole.
उत्तर
Let H be the height of the pole, makes an angle of depression from the top of the tower to top and bottom of\ poles are 45° and 60° respectively.
Let AB = H , CE = h, AD = x and DE = 50m.
`∠CBE = 45^@ and ∠DAE = 60^@`
Here we have to find height of pole.
The corresponding figure is as follows
In ΔADE
`=> tan A = (DE)/(AD)`
`=> tan 60^@ = 50/x`
`=> x = 50/sqrt3`
Again in ΔBCE
`=> tan B = (CE)/(BC)`
`=> tan 45^@ = h/x`
`=> 1 = h/x`
`=> h = 50/sqrt3`
`=> h = 28.87`
Therefore H = 50 - h
=> H = 50 - 28.87
`=> H = 21.13`
Hence height pole is 21.13 m
APPEARS IN
संबंधित प्रश्न
A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. `(sqrt 3=1.73)`
The 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 building.
A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30°respectively. Find the width of the river.
An observed from the top of a 150 m tall lighthouse, the angles of depression of two ships approaching it are 30° and 45°. If one ship is directly behind the other, find the distance between the two ships.
The angle of elevation of an aeroplane from a point on the ground is 45° after flying for 15seconds, the elevation changes to 30° . If the aeroplane is flying at a height of 2500 meters, find the speed of the areoplane.
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 2.5m from the banks, find the width of the river.
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30° to the ground. What should be the length of the slide?
Two towers A and B are standing some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be 30°. From the top of tower B, the angle of depression of the foot of tower A is found to be 60°. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is ____________ m.
A 1.5 m tall boy is standing at some distance from a 31.5 m tall building. If he walks ’d’ m towards the building the angle of elevation of the top of the building changes from 30° to 60°. Find the length d. (Take `sqrt3 = 1.73`)
A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is 45°. Find the height of the temple.
