Advertisements
Advertisements
Question
The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y.
Solution
Let AB and CD be the two towers and E be the mid-point of AC.
Height of the tower, AB = y
Height of the tower, CD = x
it is given that, ∠ AEB=60° and ∠ CED=30°
Also, `AE=EC`
In right Δ AEB,
`tan 60°= (AB)/(AE)`
⇒ `sqrt3=y/(AE)`
`⇒ AE=y/sqrt3`
In right ∆CED,
`tan 60° = (AB)/(AF)`
⇒ `1/sqrt3=x/(CE)`
`⇒CE=sqrt3x`
`y/sqrtx=sqrt3x`
`⇒ y=3x`
`⇒x/y=1/3`
`∴ x: y=1:3`
Hence, the ratio of x : y is 1 : 3.
APPEARS IN
RELATED QUESTIONS
The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them.
If the angle of elevation of cloud from a point 200 m above a lake is 30º and the angle of depression of its reflection in the lake is 60º, then find the height of the cloud above the lake
The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree, when seen from the top of the second tree, is 45°. If the height of the second tree is 80 m, find the height of the first tree.
A kite is flying at a height of 75 in from the level ground, attached to a string inclined at 60°. to the horizontal. Find the length of the string, assuming that there is no slack in it.
[Take `sqrt(3)` =1.732 ]
On a horizonal 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.
The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is
Two buildings are in front of each other on either side of a road of width 10 metres. From the top of the first building which is 20 metres high, the angle of elevation to the top of the second is 45°. What is the height of the second building?
From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree. `(sqrt(3) = 1.732)`
A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be ____________.
The top of a banquet hall has an angle of elevation of 45° from the foot of a transmission tower and the angle of elevation of the topmost point of the tower from the foot of the banquet hall is 60°. If the tower is 60 m high, find the height of the banquet hall in decimals.
