List of top Mathematics Questions on Heights and Distances

If two towers of heights h₁, and h₂ subtend angles of 30° and 60° respectively at the midpoint of the line joining their feet, then the ratio of h₁: h₂ is

A tree is broken by wind, its upper part touches the ground at a point 10 metre from the foot of the tree and makes an angle of 45° with the ground. Then what is the entire height of the tree?

A man standing on the bank of a river observes that the angle subtended by a tree standing on the opposite bank is 60° on his side of Bank. When he moved away 24 m from the bank, he finds the angle to be 30°. Find the breadth of the river:

A ladder of length 30 m is leaning against a wall making an angle of 30° with the horizontal. Find the distance between the foot of the ladder and the wall.

The base of a tower is 80m away from a point A on the ground. If the angle of elevation of the top of the tower from A is 45. Calculate the height of the tower.

A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to be subtend an angle twice as before. Find the height of the tower?

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of the hill is -

Two ships are sailing in the Sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 100m high, the distance between the two ships is:

Find length of a kite string flying at 100 m above the ground with the elevation 60°.

The tops of two poles are of height 20 m and 14 m are connected by a wire. If the wire makes an angle 30° with the horizontal, then the length of the wire is

The length of the shadow of a vertical pole is \(\sqrt 3\) times its original length. The angle of elevation to the sun is ____ .

If two towers of heights h1 and h2 subtend angles of 45° and 30° respectively at the midpoint of the line joining their feet, then the ratio of h₁: h₂ is

The angle of elevation of the sun, when shadow of a pole of 'h' metre height is \(\sqrt{3}\)h metre long is

Two poles of height 6 m and 11 m stand on a plain ground and the distance between their feet is 12 m, then the distance between their tops is

Distance between the points (0, a) and (0, -a) is

If the angle of elevation of the Sun is 60°, then the ratio of a tree with its shadow is

From the top of the tower 60 mts high the angle of depression of two objects due north and due south of the tower are 60° and 45° then the distance between two objects is 60

The length, breadth and height of a room are 10 m, 10√2 m and 10 m respectively. The angle of elevation of a top corner of room from any point on a diagonal of the base of the room is

A man is standing between two lamp posts on a horizontal line dividing the distance between them in the ratio 1:2. The height of man is 2 m. It is noticed that shadow of the man with respect to first lamp post just touches the foot of second lamp post. If the distance between the posts is 30 m, find the height of the first post.

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

A toy is in the shape of a hemisphere surmounted by a cone. If radius of base of the cone is 3 cm and its height is 4 cm, the total surface area of the toy 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 60⁰ and when he walks 40 metres away from the tree the angle of elevation becomes 30⁰. The breadth of the river is

A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45⁰. Then which of the following statements is correct?

The angles of elevation of the top of a tower, from the top and the foot of a pole of height 10 m, are 30⁰ and 60⁰ respectively. The height of the tower is

The Qutab Minar casts a shadow 150 m long at the same time when the Vikas Minar casts a shadow 120 m long on the ground. If the height of the Vikas Minar is 80 m, find the height of the Qutab Minar.