Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let the difference between two trees be DE = 60 m and angle of depression of the first tree from the top to the top of the second tree is ∠ABC = 45°.
Let BE = H m, AC = h m, AD = 80m.
We have to find the height of the first tree
The corresponding figure is as follows
In ΔABC
`=> tan B = (AC)/(BC)`
`=> tan 45° = h/60`
`=> 1 - h/60`
`=> h = 60`
Since H = 80 - h
=> H = 80 - 60
=> H = 20
Hence the heght of first tree is 20 m
APPEARS IN
संबंधित प्रश्न
The angle of elevation of an aeroplane from point A on the ground is 60˚. After flight of 15 seconds, the angle of elevation changes to 30˚. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.
From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be a and 3. If the height of the lighthouse be h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance
`(h(tan alpha + tan beta))/(tan alpha tan beta)` meters
The length of shadow of a tower on the plane ground is `sqrt3` times the height of the tower.
The angle of elevation of sun is:
If the ratio of the height of a tower and the length of its shadow is `sqrt3:1`, what is the angle of elevation of the Sun?
From a point on the ground, 20 m away from the foot of a vertical tower, the angle elevation of the top of the tower is 60°, What is the height of the tower?
From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is
A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such away that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Determine the speed at which the bird flies `(sqrt(3) = 1.732)`
The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°, then the distance between the two towers is ____________.
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged.
Find the angle of elevation of the sun when the shadow of a pole h metres high is `sqrt(3)` h metres long.
