Advertisements
Advertisements
Question
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 45°. If the tower is 30 m high, find the height of the building.
Solution
Let AB be the building and CD be the tower.
In ΔCDB,
`(CD)/(BD)=tan45^@`
`=>30/(BD)=1`
⇒BD=30 m
In ΔABD,
`(AB)/(BD)=tan30^@`
⇒AB=BD × `1/sqrt3`
`=>AB=30/sqrt3=10sqrt3m`
Therefore, the height of the building is `10sqrt3m`
APPEARS IN
RELATED QUESTIONS
The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill.
On a horizontal plane, there is a vertical tower with a flagpole on the top of the tower. At a point 9 meters away from the foot of the tower the angle of elevation of the top and bottom of the flagpole are 60° and 30° respectively. Find the height of the tower and the flagpole mounted on it.
A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.
The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. Use`[sqrt3=1.732]`
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is
Find the distance between the points (a, b) and (−a, −b).
A man is standing on the deck of a ship, which is 40 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill `(sqrt(3) = 1.732)`
A tower is 60 m heigh. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45°. What is the height of the tower?
The angles of depression of two objects from the top of a 100 m hill lying to its east are found to be 45° and 30°. Find the distance between the two objects. (Take `sqrt3 = 1.73`)
