R d sharma solutions mathematics class 10 Solutions for Chapter 11 some applications of trigonometry

A ladder 15 metres long reaches the top of a vertical wall. If the ladder makes an angle of 60^o with the wall, find the height of the wall.

A tower stands vertically on the ground. From a point on the ground, 20 m away from the foot of the tower, the angle of elevation of the top the tower is 60°.

What is the height of the tower?

The angle of elevation of a ladder against a wall is 60° and the foot of the ladder is 9.5 m away from the wall.

Find the length of the ladder.

A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60° with the level of the ground.

Determine the height of the wall.

An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45° with the horizontal through the foot of the pole, find the length of the wire.

A kite is flying at a height of 75 meters from the ground level, attached to a string inclined at 60° to the horizontal.

Find the length of the string to the nearest meter.

A vertical tower stands on a horizontal place and is surmounted by a vertical flag staff. At a point on the plane 70 meters away from the tower, an observer notices that the angles of elevation of the top and bottom of the flag-staff are respectively 60° and 45°.

Find the height of the flag staff and that of the tower.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height 5 meters. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are respectively 30° and 60°.

Find the height of the tower.

A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

A person observed the angle of elevation of a tower as 30°. He walked 50 m towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as 60°.

Find the height of the tower.

The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°.

Find the height of the tower.

A parachute is descending vertically and makes angles of elevation of 45° and 60° at two observing points 100 m apart from each other on the left side of himself.

Find the maximum height from which he falls and the distance of point where he falls on the ground from the just observation point.

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, find the distance between the objects.

A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30° respectively.

Find the width of the river.

The angle of elevation of a tower from a point on the same level as the foot of the tower is 30°. On advancing 150 meters towards the foot of the tower, the angle of elevation of the tower becomes 60°.

Show that the height of the tower is 129.9 metres.

The angle of elevation of the top of a tower as observed from a point in a horizontal plane through the foot of the tower is 32°. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 63°.

Find the height of the tower and the distance of the first position from the tower.

[Take tan 32° = 0.6248 and tan 63° = 1.9626]

The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 meters towards the foot of the tower to a point B the angle of elevation increases to 60°.

Find the height of the tower and the distance of the tower from the point A.

From the top of a building 15 m high the angle of elevation of the top of tower is found to be 30°. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°.

Find the height of the tower and the distance between the tower and the building.

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 m away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively.

Find the height of the tower and the flag pole mounted on it.

A tree breaks due to 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 between the foot of the tree to the point where the top touches the ground is 8 m.

Find the height of the tree.

From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag staff from P is 45°.

Find the length of the flag staff and the distance of the building from the point P.

A vertical tower stands on a horizontal plane and is surmounted by a flag staff of height 7m. From a point on the plane, the angle of elevation of the bottom of flag staff is 30° and that of the top of the flag staff is 45°.

Find the height of the tower.

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.8 m on the ground.

Find the height of the lamp post by using trigonometric ratio.

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.8 m on the ground.

Find the height of the lamp post by using properties of similar triangles.

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building.

Find the distance he walked towards the building.

The shadow of a tower standing on level ground is found to be 40 m longer when Sun’s altitude is 30° than when it was 60°.

Find the height of the tower.

From a point on the ground the angle of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are 45° and 60° respectively.

Find the height of the transmission tower.

The angle of depression of the top and bottom of 8 m tall building from the top of a multistoried building are 30° and 45°.

Find the height of the multistoried building and the distance between the two buildings.

A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°.

Find the height of the pedestal.

A T.V. tower stands vertically on a bank of a river of a river. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From a point 20 m away this point on the same bank, the angle of elevation of the top of the tower is 30°.

Find the height of the tower and the width of the river.

From the top of a 7 m high building, the angle of elevation of the top of a cable is 60° and the angel of depression of its foot is 45°. Determine the height of the tower.

As observed from the top of a 75 m tall lighthouse, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

The angle of elevation of the top of the building from the foot of the tower is 30° and the angle of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

From a point on a bridge across a river the angle of depression of the banks on opposite side of the river are 30° and 45° respectively. If the bridge is at the height of 30 m from the banks, find the width of the river.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point between them on the road the angles of elevation of the top of the poles are 60° and 30° respectively.

Find the height of the poles and the distances of the point from the poles.

The length of the shadow of a tower standing on level plane is found to be 2x meters longer when the sun’s altitude is 30° than when it was 45°.

Prove that the height of tower is x(√3+1) meters.

A tree breaks due to 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 meters.

Find the height of the tree.

A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.