CBSE Class 10 Mathematics Application of Trigonometry MCQs

Question. The angle of elevation of the top of a tower from a point on the ground, which is 20m away from the foot of the tower is 60⁰. Find the height of the tower.
(a) 10 √3 m
(b) 30 √3 m
(c) 20 √3 m
(d) none of these

Question. The height of a tower is 10m. What is the length of its shadow when Sun’s altitude is 45⁰?
(a) 10 m
(b) 30 m
(c) 20 m
(d) none of these

Question. The angle of elevation of a ladder leaning against a wall is 60⁰ and the foot of the ladder is 9.5 m away from the wall. Find the length of the ladder.
(a) 10 m
(b) 19 m
(c) 20 m
(d) none of these

Question. If the ratio of the height of a tower and the length of its shadow is √3 : 1, what is the angle of elevation of the Sun?
(a) 30⁰
(b) 60⁰
(c) 45⁰
(d) none of these

Question. What is the angle of elevation of the Sun when the length of the shadow of a vertical pole is equal to its height?
(a) 30⁰
(b) 60⁰
(c) 45⁰
(d) none of these

Question. From a point on the ground, 20 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is 600, what is the height of the tower?
(a) 10 √3 m
(b) 30 √3 m
(c) 20 √3 m
(d) none of these

Question. If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary, find the height of the tower.
(a) 10 m
(b) 6 m
(c) 8 m
(d) none of these

Question. In the below fig. what are the angles of depression from the observing positions D and E of the object A?

(a) 30⁰, 45⁰
(b) 60⁰ , 45⁰
(c) 45⁰, 60⁰
(d) none of these

Question. The ratio of the length of a rod and its shadow is 1: 3 . The angle of elevation of the sun is
(a) 30⁰
(b) 60⁰
(c) 45⁰
(d) none of these

Question. If the angle of elevation of a tower from a distance of 100m from its foot is 60⁰, then the height of the tower is
(a) 100 √3 m
(b) 200/ √3 m
(c) 50 √3 m
(d) 100/√3 m

ANSWERS

Q01. b Q02. a Q03. c Q04. a Q05. d Q06. a Q07. a

Q08. b Q09. d Q10. d Q11. d Q12. b Q13. a Q14. a

Q15. c Q16. b Q17. a Q18. c Q19. a Q20. b Q21. a

Q22. d Q23. b Q24. b Q25. d Q26. b Q27. a Q28. c

Q29. b Q30. b Q31. d Q32. b Q33. c Q34. c Q35. b

Q36. b Q37. d Q38. a Q39. c Q40. c Q41. c Q42. b 

Q43. c Q44. b Q45. b Q46. b Q47. a Q48. b

  

Question : If the altitude of the sun is at 60⁰, then the height of the vertical tower that will cast a shadow of length 30m is
(a) 30 √3 m
(b) 15 m
(c) 30 √3 m
(d) 15 √2 m

Question : A tower subtends an angle of 30⁰ at a point on the same level as its foot. At a second point ‘h’ metres above the first, the depression of the foot of the tower is 60⁰. The height of the tower is
(a) h/2 m
(b) h/3 m
(c) √3h m
(d) h/√3 m

Question : A tower is 100 3 m high. Find the angle of elevation if its top from a point 100 m away from its foot.
(a) 30⁰
(b) 60⁰
(c) 45⁰
(d) none of these

Question : The angle of elevation of the top of a tower from a point on the ground, which is 30m away from the foot of the tower is 300. Find the height of the tower.
(a) 10 √3 m
(b) 30 √3 m
(c) 20√ 3 m
(d) none of these

Question : The string of a kite is 100m long and it makes an angle of 60⁰ with the horizontal. Find the height of the kite, assuming that there is no slack in the string.
(a) 100 √3 m
(b) 200 √3 m
(c) 50 √3 m
(d) 100 √3 m

Question : A kite is flying at a height of 60m above the ground. The inclination of the string with the ground is 60⁰. Find the length of the string, assuming that there is no slack in the string.
(a) 40 √3 m
(b) 30 √3 m
(c) 20 √3 m
(d) none of these

Question : A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is 30⁰.
(a) 10 m
(b) 30 m
(c) 20 m
(d) none of these

Question : A tower is 50m high, Its shadow ix ‘x’ metres shorter when the sun’s altitude is 45⁰ than when it is 30⁰. Find the value of ‘x’
(a) 100 √3 m
(b) 200 √3 m
(c) 50 √3 m
(d) none of these

Question : Find the angular elevation of the sun when the shadow of a 10m long pole is 10 √3 m.
(a) 30⁰
(b) 60⁰
(c) 45⁰
(d) none of these

Question : A vertical pole stands on the level ground. From a point on the ground 25m away from the foot of the pole, the angle of elevation of its top is found to be 600. Find the height of the pole.
(a) 25 √3 m
(b) 25 √3 m
(c) 50 √3 m
(d) none of these

Question : A kite is flying at a height of 75m above the ground. The inclination of the string with the ground is 60⁰. Find the length of the string, assuming that there is no slack in the string.
(a) 40 √3 m
(b) 30√ 3 m
(c) 50 √3 m
(d) none of these

Question : The angle of elevation of the tope of a tree from a point A on the ground is 60⁰. On walking 20m away from its base, to a point B, the angle of elevation changes to 30⁰. Find the height of the tree.
(a) 10 √3 m
(b) 30 √3 m
(c) 20 √3 m
(d) none of these

Question : A 1.5m tall boy stands at a distance of 2m from lamp post and casts a shadow of 4.5m on the ground. Find the height of the lamp post.
(a) 3 m
(b) 2.5 m
(c) 5 m
(d) none of these

Question : The height of the tower is 100m. When the angle of elevation of the sun changes from 30⁰ to 45⁰, the shadow of the tower becomes ‘x’ meters less. The value of ‘x’ is
(a) 100 √3 m
(b) 100 m
(c) 100√( 3 – 1) m
(d) 100 /√3

Question : The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an angle of 30⁰ with horizontal, then the length of the wire is
(a) 12 m
(b) 10 m
(c) 8 m
(d) 6 m

Question : If the angles of elevation of a tower from two points distant a and b (a > (b) from its foot and in the same straight line from it are 30⁰ and 60⁰, then the height of the tower is

Question : The angles of elevation of the top of a tower from two points at a distance of ‘a’ m and ‘b’ m from the base of the tower and in the same straight line with it are complementary, then the height of the tower is

Question : From the top of a cliff 25m 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) 25 m
(b) 50 m
(c) 75 m
(d) 100 m

Question : If the angle of elevation of a cloud from a point 200m above a lake is 30⁰ and the angle of depression of its reflection in the lake is 60⁰, then the height of the cloud above the lake is
(a) 200 m
(b) 500 m
(c) 30 m
(d) 400 m

Question : The angle of elevation of a cloud from a point ‘h’ meter above a lake is ‘α’. The angle of depression of its reflection in the lake is 450. The height of the cloud is