Advertisements
Advertisements
प्रश्न
From the top of the tower h metre high , the angles of depression of two objects , which are in the line with the foot of the tower are ∝ and ß (ß> ∝ ) cts .
उत्तर
Let the two objects be at points C and D.
The angle of depression for the point C is `ßß` and for the point D is `∝∝`
In ∆ABC,
`tan ß=h/(BC)`
`⇒ BC= h /tanß `
`⇒ tan∝= h/( BC+CD)`
`⇒∝= h/(h/tanß+CD)`
`⇒h/ tanß+CD= h/tan∝`
`⇒ CD= h/tan∝-h/tanß`
`⇒ CD=h [1/tan∝-1/tanß]`
`⇒CD=h [cot ∝-cot ß]`
APPEARS IN
संबंधित प्रश्न
The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x, y.
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.
The angle of elevation of an aeroplane from a point on the ground is 45°. After a flight of 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 3000 metres, find the speed of the aeroplane.
Two boats approach a lighthouse in mid-sea from opposite directions. The angles of elevation of the top of the lighthouse from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the lighthouse.
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find
(i) how far the pole is from the bottom of a tower,
(ii) the height of the pole. (Use \[\sqrt{3} = 1 . 732\])
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.
An observer , 1.7 m tall , is` 20 sqrt3` m away from a tower . The angle of elevation from the eye of an observer to the top of tower is 300 . Find the height of the tower.
An observer, 1.5 m tall, is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer.
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
A pole 6 m high casts a shadow `2sqrt(3)` m long on the ground, then the Sun’s elevation is ______.
