Welcome to your Some Applications of Trigonometry MCQs Mock Test of 10th Class Mathematics

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1. If the angles of elevation of the top of a tower from two points at the distance of a m and b m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is

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2. If the length of the shadow of a tower is increasing, then the angle of elevation of the sun

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

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4. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will

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5. The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. The angle of elevation of the Sun is

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6. If the height of a tower and the distance of the point of observation from its foot,both, are increased by 10%, then the angle of elevation of its top

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7. A tree breaks due to a 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. The height of the tree is

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8. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be

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9. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will be

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10. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high.Determine the angle of elevation of the top of the tower from the eye of the observer.

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11. The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is:

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12. 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 tower is:

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13. If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is

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14. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

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15. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower

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16. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°, then the distance between the two towers is:

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17. The angle of elevation of the top of a vertical tower from a point on the ground is60°. From another point 10 m vertically above the first, its angle of elevation is45°. Find the height of the tower.

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18. There are two windows in a house. A window of the house is at a height of 1.5 m above the ground and the other window is 3 m vertically above the lower window. Ram and Shyam are sitting inside the two windows. At an instant, the angle of elevation of a balloon from these windows are observed as 45° and 30° respectively. Find the height of the balloon from the ground.

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Question 19. If at some time, the length of the shadow of a tower is √3 times its height, then the angle of elevation of the sun, at that time is:

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Question 20. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is:

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Question 21. At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is:

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Question 22. A person is flying a kite at a height of 30 m from the horizontal level. The length of string from the kite to the person is 60 m. Assuming that here is no slack in the string, the angle of elevation of kite to the horizontal level is:

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Question 23. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of tower (in m) is:

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Question 24. A man at the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance travelled by the car during this time interval is:

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Question 25. The angle of elevation of the top of a 15 m high tower at a point 15 m away from the base of tower is: