CBSE GRADE-10 - MATHS WORK SHEET - Application of trigonometry

 GRADE -10- MATHEMATICS - PREVIOUS YEAR QUESTIONS CHAPTERWISE 

Chapter 1 - Applications of trigonometry  

Grade: X -Mathematics

Previous year Questions

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1.     A ladder, leaning against a wall, makes an angle of 60^o with the horizontal. If the foot of the ladder is 2.5m away from the wall, find the length of the ladder.

2.     An observer, 1.7m tall, is 20√3 away from a tower. The angle of elevation from  the eye of observer to the top of tower is 30^o. Find the height of the tower.

3.     The angles of depression of the top and bottom of a 50m high building from the top of a tower are 45^o and 60^o respectively. Find the height of the tower and the horizontal distance between the tower and the building. ( use √3 =1.73)

4.     A man standing on the deck of a ship, which is 10m above water level, observes the angle of elevation of the top of a hill as 60^o and the angle of depression of the base of hill as 30^o. Find the distance of the hill from the ship and height of the hill.

5.     Two men on either side of a 75m high building and in line with base of building observe the angles of elevation of the top of the building as 30 and 60. Find the distance between the two men. (use √3 =1.73)

6.     A 7 m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60 and 45 respectively. Find the height of the tower correct to one place of decimal. (use √3 =1.73)

7.     An aeroplane, when flying at a height of 4000m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60 and 45 respectively. Find the vertical distance between the aeroplane at that instant. (Take √3 =1.73)

8.     A bird is sitting on the top of a 80m high tree. From a point on the ground, the angle of elevation of the bird is 45. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30. Find the speed of the flying bird.(use √3 =1.73)

9.     The angle of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are 60 and 30 respectively. Find the height of the tower.

10.      The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60. From a point Y, 40m vertically above X, the angle of elevation of the top Q of tower is 45. Find the height of the tower PQ and the distance PX. (use √3 =1.73)

11. An observer from the top of a light house, 100m high above sea level, the angles of depression of a ship, sailing directly towards it, changes from 30 to 60. Find the distance travelled by the ship during the period of observation.

12. From a point on the ground, the angle of elevation of the top of a tower is observed to be 60. From a point 40m vertically above the first point of observation, the angle of elevation of the top of the tower is 30. Find the height of the tower and its horizontal distance from the point of observation.

13. A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 5m. From a point on the ground the angles of elevation of the top and bottom of the flagstaff are 60 and 30 respectively. Find the height of the tower and the distance of the point from the tower. (use √3 =1.73)

14. The tops of two towers of height x and y, standing on level ground, subtend angles        

    of 30 and 60 respectively at the centre of the line joining their feet, then find x : y.

15. A tower AB is 20m high and BC, its shadow on the ground, is 20√3 m long. Find

     the Sun’s altitude.

16. A pole casts a shadow of length 20√3 m on the ground, when the sun’s elevation is 60. Find the height of the pole.

17. The angle of elevation of the top of a building from the foot of the tower is 30 and the angle of deviation of the top of the tower from the foot of the building is 45. If the tower is 30m high, find the height of the building.

18. The angle of elevation of an aeroplane from a point A on the ground is 60. After a flight of 15 seconds, the angle of elevation changes to30. If the aeroplane is flying at a constant height of 1500√3m, find the speed of the plane in km/hr.

19. From the top of a tower of height 50m, the angles of depression of the top and bottom of a pole are 30 and 45 respectively. Find (i) how far the pole is from the bottom of a tower. (ii) the height of the pole. (use √3 =1.73)

20. From a point P on the ground the angle of elevation of the top of a tower is 30 and that of the top of a flagstaff fixed on the top of the tower, is 60. If the length of the flagstaff is 5m, find the height of the tower.

21. At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30. The angle of depression of the reflection of the cloud in the lake, at A is 60. Find the distance of the cloud from A.

22. Two poles of equal heights are standing opposite to each other on either side of the road which is 80m wide. From a point P between them on the road, the angle of elevation of the top of a pole is 60 and the angle of depression from the top of another pole at point P is 30. Find the heights of the poles and the distance of the point P from the poles.

23. Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships as observed from the top of the light house are 60 and  45. If the height of the light house is 200m, find the distance between the two ships. (use √3 =1.73)

24. The angle of elevation of  an  aeroplane from a point on the ground is 60. After a flight of 30 seconds the angle of elevation becomes 30.  If the aeroplane is flying at a constant height of 3000√3m, find the speed of the aeroplane.

25. Two ships are approaching a lighthouse from opposite directions. The angles of depression of the two ships from the top of the lighthouse are 30 and 45. If the distance between the two ships is 100m, find the height of the lighthouse. (use √3 =1.73)

26. The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60m high, are 30 and 60 respectively. Find the difference between the heights of the building and the tower and the distance between them.

27. From the top of a 60m high building, the angles of depression of the top and the bottom of a tower are 45 and 60 respectively. Find the height of the tower. (use √3 =1.73)

28. The angle of elevation of the top of a tower at a distance of 120m from a point A on the ground is 45. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60, then the height of the flagstaff. (use √3 =1.73)

29. The angle of elevation of the top of a chimney from the foot of a tower is 60 and the angle of depression of the foot of the chimney from the top of the tower is 30. If the height of the tower is 40m, find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should by 100m. State if the height of the above mentioned chimney meets the pollution norms. What value is discussed in this question?

30. The horizontal distance between two poles is 15m. The angle of depression of the top of first pole as seen from the top of second pole is 30. If the height of the second pole is 24m, find the height of the first pole. (use √3 =1.73)

31. As observed from the top of a 60m high lighthouse from the sea-level, 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. (use √3 =1.73)

32. The angles of elevation of the top of a tower from two points at a distance of 6m and 13.5m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.

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

34. From a point P on the ground, the angle of elevation of the top of a 10m tall building is 30. A flagstaff is fixed at the top of the building and the angle of elevation of the top of the flagstaff from point P is 45. Find the length of the flagstaff and the distance of the building from the point P. (use √3 =1.73)

35. Two poles of equal heights are standing opposite each other on either side of the road, which is 80m 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.

36. From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 30. Determine the height of the tower.

37. The shadow of a tower standing on a level ground is found to be 20m longer when the sun’s altitude is 45 than when it is 60. Find the height of the tower.

38. The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be 45 and 30. If the ships are 200m apart, find the height of the lighthouse.

39. A kite is flying at a height of 45m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60. Find the length of the string assuming that there is no slack in the string.

40.The angle of depression of the top and bottom of a tower as seen from the top of a 60√3m high cliff are 45 and 60 respectively. Find the height of the tower.

41. From the top of a tower 50m high, the angle of depression of the top of a pole is 45 and from the foot of the pole, the angle of elevation of the top of the tower is 60. Find the height of the pole if the pole and tower stand on the same plane.

42.The angle of depression from the top of a tower of a point A on the ground is 30. On moving a distance of 20m from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60. Find the height of the tower and its distance from the point A.

43. The angle of elevation of the op 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, find the height of the hill.

44. The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60m high building are 30 and 60 respectively. Find (i) the difference between the heights of the lighthouse and the building. (ii) the distance between the lighthouse and the building.

45. From the top of a tower 100m high, a man observes two cars on the opposite sides of the tower with angles of depression 30 and 45 respectively. Find the distance between the cars. (use √3 =1.73)

46. From the top of a vertical tower, the angles of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45 and 60. If the cars are 100m apart and are on the same side of the tower, find the height of the tower.(Use use √3 =1.73)

47. A ladder of length 6m makes an angle of 45 with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60 with the floor. Find the distance between these two walls of the rooms.

48. Two poles of equal heights are standing opposite to each other on either side of the road, which is 100m 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.

49. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 10m high building are 30 and 60 respectively. Find the height of the tower.

50. From the top of a 15m high building, the angle of elevation of the top of a cable tower is 60 and the angle of depression of its foot is 30. Determine the height of the tower.

51. The angle of elevation of the top of a vertical tower from a point on the ground is 60. From another point 10m vertically above the first, its angle of elevation is 30. Find the height of the tower.

52. The angles of depression of the top and bottom of a 12m tall building, from the top of a multi-storeyed building are 30 and 60 respectively. Find the height of the multi-storeyed building.

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

54. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30, which is approaching the foot of the tower with a uniform speed. 10 seconds later, the angle of depression of the car is found to be 60. Find the time taken by the car to reach the foot of the tower from this point.

55. A man standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60. When he moves 40m away from the bank, he finds the angle of elevation to be 30. Find the height of the tree.

56. The shadow of a tower standing on a level ground is found to be 30m longer when the sun’s altitude is 30 than when it is 60. Find the height of the tower.

57. From the top of a 7m high building, the angle of elevation of the top of a tower is 60 and the angle of depression of the foot of the tower is 30. Find the height of the tower.

58. The angle of elevation of a cloud from a point 60m above a lake is 30 and the angle of depression of the reflection of the cloud in the lake is 60. Find the height of the cloud from the surface of the lake.

59. A man on the deck of a ship, 12m above water level, observes that the angle of elevation of the top of a cliff is 60 and the angle of depression of the base of the cliff is 30. Find the distance of the cliff from the ship and the height of the cliff.

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