Class 10 Maths – Some Applications of Trigonometry Quiz

A group of students of class X visited India Gate on an education trip. India Gate is about 42 metres in height. If the students are standing at a distance of 42 m away from the monument, the angle of elevation of the top of the monument is:

For the India Gate monument of height 42 m, if the line of sight to its top makes an angle of elevation of 60° with the horizontal, then the distance (in metres) at which the students should stand from the foot of the monument is: (Use \(\sqrt{3} = 1.732\))

If the altitude of the Sun is 60°, then the height of the vertical tower that casts a shadow of length 20 m on the ground is:

The ratio of the length of a rod and its shadow is 1 : 1. The angle of elevation of the Sun is:

The angle formed by the line of sight with the horizontal, when the object viewed is below the horizontal level, is:

If a pole 6 m high casts a shadow \(2\sqrt{3}\) m long on the ground, then the angle of elevation of the Sun is:

The angle of elevation of the top of a 30 m high tower at a point 30 m away from the base of the tower is:

From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is observed to be 60°. The height of the tower (in metres) is:

At a particular time of the day, the length of the shadow of a tower is equal to its height. Then, the angle of elevation of the Sun at that time (the Sun's altitude) is:

A vertical pole of length 7.5 m casts a shadow 5 m long on the ground. At the same time, a tower casts a shadow 24 m long on the ground. The height of the tower is:

The ratio of the length of a pole and its shadow on the ground is \(1 : \sqrt{3}\). The angle of elevation of the Sun is:

A pole \(7\sqrt{3}\) m high casts a shadow 21 m long on the ground. The elevation of the Sun at that moment is:

A lamp post 9 m high casts a shadow \(3\sqrt{3}\) m long on the ground. The Sun's elevation at this moment is:

At a time when the angle of elevation of the Sun is 45°, a tree casts a shadow 7 m long on the ground. The height of the tree is:

From the top of a 75 m high lighthouse, the angle of depression of a ship at sea is 30°. The horizontal distance of the ship from the base of the lighthouse is:

A kite is flying at a height of 75 m above the ground. The string attached to the kite is taut and makes an angle of 45° with the horizontal. The length of the string is:

From the top of a 75 m high lighthouse at sea level, the angles of depression of two ships are 45° and 30°. If the two ships are exactly in a straight line, one behind the other on the same side of the lighthouse, then the distance between the two ships is:

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

A 20 m long ladder is placed against a vertical wall, with its foot on level ground and the other end resting on the wall. If the ladder makes an angle of 60° with the ground, the height reached by the ladder on the wall is:

From the top of a vertical tower of height 50 m, the angles of depression of the top and the bottom of a building are 30° and 60° respectively. The height of the building is: