Advertisements
Advertisements
प्रश्न
The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are respectively 30° and 45°. Find the height of the rock.
उत्तर
Let AB be the height of Rock which is Hm. and makes an angle of elevations 45° and 30° respectively from the bottom and top of the tower whose height is 100 m.
Let AE = hm, BC = x m and CD = 100.
∠ACB = 45°, ∠ADE = 30°
We have to find the height of the rock
We have the corresponding figure as
So we use trigonometric ratios.
In ΔABC
`tan 45^@ = (AB)/(BC)`
`=> 1- (100 + h)/x`
`=> x = 100 + h`
Again in Δ ADE
`tan 30^@ = (AE)/(DE)`
`=> 1/sqrt3 = h/x`
`=> 100 + h = sqrt3h`
=> h = 136.65
H = 100 + 136.65
=> H = 236.65
Hence the height of rock is 236.65 m
APPEARS IN
संबंधित प्रश्न
The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the angle of elevation becomes 300 If the aeroplane is flying at a constant height of 3000 3 m, find the speed of the aeroplane.
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3. The radii of the top and bottom circular ends are 20 cm and 12 cm, respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (use π = 3.14)
From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower.
A tree is broken by the wind. The top of that tree struck the ground at an angle of 30° and at a distance of 30. Find the height of the whole tree
The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation of the top is 45°. Calculate the height of the tower.
A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a so that it slides a distance b down the wall making an angle β with the horizontal. Show that `a/b = (cos alpha - cos beta)/(sin beta - sin alpha)`
An observer, 1.5 m tall, is 28.5 m away from a tower 30 m high. Determine the angle of elevation of the top of the tower from his eye.
Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30 and 45 respectively. If the height of the tower is 50 meters, find the distance between the two men.
The shadow of a tower at a time is three times as long as its shadow when the angle of elevation of the sun is 60°. Find the angle of elevation of the sun at the time of the longer shadow ?
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.
