Advertisements
Advertisements
प्रश्न
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?
उत्तर
Let AB and CD represent two buildings. AB = 20 m, BC is the width of the road.
BC = 10 m
m∠MAD = 45° ---- (angle of elevation)
ABCM is a rectangle.
AM = BC = 10 m ---(1)
AB = MC = 20 m ---(2)
Let MD = x,
Then in right angled ΔAMC,
tan ∠MAD = tan 45° = `"MD"/"MA"`
∴ `1 = x/10`
∴ x = 10
Now,
CD = CM + MD = 20 + 10 = 30 m.
Thus the height of the second building is 30 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.
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.
If a vertical pole 6m high has a shadow of length 2 √3 metres, find the angle of elevation of the sun.
The altitude of the sun at any instant is 60º. Find the height of the vertical pole that will cast a shadow of 30 m.
From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30º. The angle of elevation of the top of a water tank (on the top of the tower) is 45º. Find the (i) height of the tower (ii) the depth of the tank.
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.
A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 600 to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.
PQ is a post of given height a, and AB is a tower at some distance. If α and β are the angles of elevation of B, the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.
Two buildings are facing each other on a road of width 12 metre. From the top of the first building, which is 10 metre high, the angle of elevation of the top of the second is found to be 60°. What is the height of the second building ?
Two poles are 'a' metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is
A flag pole ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find the height of the pole `(sqrt(3) = 1.732)`
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 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)`
The angle of elevation of a cloud from a point h metres above a lake is β. The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is
Two ships are sailing in the sea on either side of the lighthouse. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the distance between the ships is `200[(sqrt(3) + 1)/sqrt(3)]` metres, find the height of the lighthouse.
In given figure, the value of CE is ____________.
In given figure, the length of AP is ____________.
A Technician has to repair light on a pole of height 10 m. She needs to reach a point 1 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60∘ to the ground, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder?
The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Then the height of the tower is ____________.
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is ______.
