Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 20 - Heights and distances [Latest edition]

The angle of elevation of a ladder leaning against a vertical wall is 60°, and the foot of the ladder is 9.6 m from the wall. Find the length of the ladder.

A ladder leaning against a vertical wall makes an angle of 30° with ground. The foot of the ladder is 3 m from the wall. Determine the length of the ladder.

The length of the shadow of a vertical pole is `sqrt(3)` times its height. Find the angle of elevation of sun.

A tower 30 m high has its shadow `30sqrt(3)` m at any time. Find the sun’s altitude.

The angle of elevation of the top of a building from a point 50 m away from its foot is 60°. Find the height of the building.

A kite is flying at a height of 90 m from the ground level, attached to a string inclined at 60° angle to the horizontal. Find the length of the string.

An observer 1.5 m tall is 48.5 m away from a pole. The angle of elevation of the top of the pole from his eye is 45°. Find the height of the pole.

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 it. The distance between the foot of the tree to the point where the top touches the ground is 6 m. Find the height of the tree before broken.

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

From the top of tower 60 m high, the angles of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. Find the height of the pole.

An aeroplane when 3,000 meters high passes vertically above another aeroplane at an instance when their angles of elevation at the same observation point are 60° and 45° respectively. How many meters higher is the one than the other?

There is a pole of height 40 m at the top of a mountain. At a point on the ground level, the angles of elevation of the top and base of the pole are 60° and 45° respectively. Find the height of the mountain.

A statue, 1.6 m tall, stands on a top of pedestal, from a point on the ground, the angle of elevation of the top of 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.

The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 200 m apart, find the height of the light house.

The length of a shadow of a tower standing on a level plane is found to be 2y meters longer when the sun’s altitude is 30° then when it was 45°. Prove that the height of the tower is `y(sqrt(3) + 1)` meters.

The angle of elevation of the top of a tower from a point A on the ground is 30°. Moving a distance of 20 metres 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.

An aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.

The angle of elevation from a point P of the top of a tower QR, 50 m high is 60°, and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest meter.

Two lamp-posts AB and CD each of height 100 m are on either side of the road. P is a point on the road between the two lamp-posts. The angles of elevation of the top of the lamp-posts from the point P are 60° and 40°. Find the distance PB and PD.

From the top of a cliff, the angle of depression of the top and bottom of a tower are observed to be 45° and 60° respectively. If the height of the tower is 20 m. Find:

1. the height of the cliff.
2. the distance between the cliff and the tower.

The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.

An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be 45° and 60° respectively. Find the width of the river. Write the answer correct to the nearest whole number.

From the top of a tower 100 m high a man observes the angles of depression of two ships A and B, on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line find the distance between the two ships A and B to the nearest metre.

(Use Mathematical Tabels for this question)

A man on the top of vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower? (Give your answer correct to nearest seconds).

As observed from the top of a light house, 100 m above the sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation.

From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. Find the height of the pole.

From a window (60 m high above the ground) of a house in a street the angles of elevation and depression of the top and the foot of another house on opposite side of street are 60° and 45° respectively. Show that the height of the opposite house is `60(1 + sqrt(3))` m.

A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.

An observed from the top of a 150 m tall light house, the angles of depression of two ships approaching it are 30° and 45°. If one ship is directly behind the other, find the distance between the two ships.

A man on deck of a ship is 10 m above the water level. He observes that the angle of elevation at the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate the distance of the cliff from the ship and height of the cliff.

A man is standing on the deck of a ship, which is 8 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.

The angle of elevation of an aeroplane from A on the grounds is 45°. After 15 seconds flight, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 3000 m, find the speed of the plane.

The angle of elevation of a cloud from a point 200 metres above the lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.

The angle of elevation of the top of a 100 m high tree from two points A and B on the opposite side of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.

The angle of elevation of the top of a tower from a point on the ground 60 m away from the foot of tower is 30°. The height of tower is ______.

A kite is flying at a height of 30 metres from the level ground, attached to a string inclined at 60° to the horizontal. The length of string is ______.

From the top of a cliff 100 m high, the angles depression of two boats on opposite sides of cliff are 30° and 60°. The distance between the boats is ______.

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is 50 m high, the height of the hill is ______.

A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the foot of the tower is 30°. The height of the tower if the height of the pole is 20 m, is ______.