MATHEMATICS CLASS- 10

MCQ- CH-9(Some applications of trigonometry)

CBSEChapter 9MCQ's

Class 10 Mathematics

Chapter 9: Some Applications of Trigonometry

50 Board-Level MCQs with Answers and Solutions

Q1. The angle formed between the horizontal line and the line of sight when an object is above the observer is called

(a) Angle of Depression
(b) Angle of Elevation
(c) Right Angle
(d) Reflex Angle

Answer: (b) Angle of Elevation

Solution: When the observer looks upward, the angle formed is called the angle of elevation.

Q2. The angle formed between the horizontal line and the line of sight when an object is below the observer is called

(a) Angle of Depression
(b) Angle of Elevation
(c) Acute Angle
(d) Obtuse Angle

Answer: (a) Angle of Depression

Q3. A man observes the top of a tower at an angle of elevation of 45°. If the distance from the tower is 20 m, then the height of the tower is

(a) 10 m
(b) 20 m
(c) 30 m
(d) 40 m

Answer: (b) 20 m

Solution: tan 45° = h/20 = 1 ⇒ h = 20 m.

Q4. Which trigonometric ratio is generally used when height and horizontal distance are known?

(a) sin θ
(b) cos θ
(c) tan θ
(d) cosec θ

Answer: (c) tan θ

Q5. The angle of elevation of the sun when a vertical pole casts no shadow is

(a) 0°
(b) 30°
(c) 45°
(d) 90°

Answer: (d) 90°

Q6. A ladder 10 m long reaches the top of a wall. If it makes an angle of 30° with the ground, the height of the wall is

(a) 5 m
(b) 5√3 m
(c) 10 m
(d) 20 m

Answer: (a) 5 m

Solution: sin 30° = h/10 ⇒ h = 5 m.

Q7. A tower is viewed from a point 30 m away at an angle of elevation of 45°. Its height is

(a) 15 m
(b) 20 m
(c) 30 m
(d) 45 m

Answer: (c) 30 m

Q8. Which chapter mainly uses trigonometric ratios to find heights and distances?

(a) Statistics
(b) Coordinate Geometry
(c) Applications of Trigonometry
(d) Circles

Answer: (c)

Q9. The line joining the observer's eye to the object is called

(a) Horizontal Line
(b) Line of Sight
(c) Vertical Line
(d) Tangent

Answer: (b)

Q10. A tree is 15 m high. The angle of elevation of its top from a point is 45°. The distance of the point from the tree is

(a) 10 m
(b) 12 m
(c) 15 m
(d) 20 m

Answer: (c) 15 m

Q11. A vertical pole casts a shadow equal to its height. The angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (b) 45°

Q12. A ladder leaning against a wall forms a right triangle with the wall and ground. The ladder represents

(a) Base
(b) Perpendicular
(c) Hypotenuse
(d) Radius

Answer: (c)

Q13. If the angle of elevation increases, keeping distance fixed, the height of the object

(a) Decreases
(b) Remains same
(c) Increases
(d) Becomes zero

Answer: (c)

Q14. A tower is 40 m high. Its angle of elevation from a point is 45°. Distance of the point from the tower is

(a) 20 m
(b) 30 m
(c) 40 m
(d) 50 m

Answer: (c)

Q15. If angle of elevation is 60° and distance from the tower is 10 m, then height of tower is

(a) 5√3 m
(b) 10√3 m
(c) 20√3 m
(d) 30 m

Answer: (b)

Solution: h = 10 tan 60° = 10√3 m.

Q16. Which trigonometric ratio relates height and hypotenuse?

(a) sin θ
(b) cos θ
(c) tan θ
(d) sec θ

Answer: (a)

Q17. Which trigonometric ratio relates base and hypotenuse?

(a) sin θ
(b) tan θ
(c) cos θ
(d) cosec θ

Answer: (c)

Q18. The angle of depression from the top of a lighthouse to a boat is 30°. Then angle of elevation of the lighthouse from the boat is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (a)

Q19. If a pole is 12 m high and its shadow is 12√3 m, the angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (a)

Q20. The horizontal line through the observer's eye is called

(a) Base Line
(b) Line of Sight
(c) Horizontal Line
(d) Perpendicular

Answer: (c)

Q21. (CBSE PYQ) A tower 50 m high is observed from a point at an angle of elevation 45°. Distance from the point to the tower is

(a) 25 m
(b) 50 m
(c) 75 m
(d) 100 m

Answer: (b)

Q22. A building is viewed at an angle of elevation of 30° from a point 20√3 m away. Height of building is

(a) 10 m
(b) 20 m
(c) 30 m
(d) 40 m

Answer: (b)

Q23. If the height of a tower doubles while distance remains same, angle of elevation will

(a) Increase
(b) Decrease
(c) Remain same
(d) Become zero

Answer: (a)

Q24. A kite is flying at a height of 50 m and the string makes an angle of 30° with the ground. Length of string is

(a) 50 m
(b) 75 m
(c) 100 m
(d) 120 m

Answer: (c)

Q25. If a tree casts a shadow of length equal to √3 times its height, the angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (a)

Q26. (CBSE PYQ) A ladder 20 m long reaches the top of a wall and makes an angle of 60° with the ground. Height reached is

(a) 10 m
(b) 10√3 m
(c) 20√3 m
(d) 40 m

Answer: (b)

Q27. Which angle is formed when looking upward towards the top of a building?

(a) Right Angle
(b) Angle of Depression
(c) Angle of Elevation
(d) Reflex Angle

Answer: (c)

Q28. Which angle is formed when looking downward from a balcony?

(a) Angle of Elevation
(b) Angle of Depression
(c) Acute Angle
(d) Straight Angle

Answer: (b)

Q29. A pole 8 m high casts a shadow of 8 m. The angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (b)

Q30. The height of a tower is 30 m and angle of elevation from a point is 60°. Distance from tower is

(a) 10√3 m
(b) 20√3 m
(c) 10 m
(d) 30√3 m

Answer: (a)

Q31. If angle of elevation is 30° and height is 10 m, horizontal distance is

(a) 5√3 m
(b) 10√3 m
(c) 20√3 m
(d) 30√3 m

Answer: (b)

Q32. A person standing 50 m from a tower sees its top at 45°. Height of tower is

(a) 25 m
(b) 50 m
(c) 75 m
(d) 100 m

Answer: (b)

Q33. The branch of mathematics used to determine inaccessible heights and distances is

(a) Algebra
(b) Statistics
(c) Trigonometry
(d) Geometry

Answer: (c)

Q34. A building is 25 m high. If angle of elevation from a point is 45°, distance from building is

(a) 20 m
(b) 25 m
(c) 30 m
(d) 35 m

Answer: (b)

Q35. Which trigonometric ratio is most commonly used in height and distance problems?

(a) sin θ
(b) cos θ
(c) tan θ
(d) cosec θ

Answer: (c)

Q36. (CBSE PYQ) A tree 10√3 m high casts a shadow of 10 m. The angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (c)

Q37. If angle of depression is 45°, then angle of elevation is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (b)

Q38. The line of sight and horizontal line together form

(a) Angle of Elevation or Depression
(b) Radius
(c) Diameter
(d) Chord

Answer: (a)

Q39. If distance from a tower is doubled, keeping height fixed, angle of elevation will

(a) Increase
(b) Decrease
(c) Remain same
(d) Become 90°

Answer: (b)

Q40. A ladder 13 m long reaches a window 5 m above the ground. Distance of ladder foot from wall is

(a) 10 m
(b) 11 m
(c) 12 m
(d) 13 m

Answer: (c)

Q41. A tower is observed at an angle of elevation of 30° from a point 30 m away. Height of tower is

(a) 10√3 m
(b) 20√3 m
(c) 30√3 m
(d) 40√3 m

Answer: (a)

Q42. (CBSE PYQ) A pole and its shadow are equal in length. The angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (b)

Q43. In applications of trigonometry, the object height generally represents

(a) Base
(b) Perpendicular
(c) Hypotenuse
(d) Radius

Answer: (b)

Q44. A bird is sitting on a pole. The angle formed when an observer looks at the bird from ground level is

(a) Angle of Depression
(b) Angle of Elevation
(c) Reflex Angle
(d) Straight Angle

Answer: (b)

Q45. The shadow of a tower is half its height. Angle of elevation of the sun is

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (c)

Q46. If tan θ = 1, then θ =

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (b)

Q47. If angle of elevation is 90°, then the object is

(a) On the horizon
(b) Directly above the observer
(c) Behind the observer
(d) Not visible

Answer: (b)

Q48. Height and distance problems are generally based on

(a) Similar Triangles and Trigonometric Ratios
(b) Probability
(c) Statistics
(d) Quadratic Equations

Answer: (a)

Q49. If the angle of elevation of a tower from a point is 60° and the distance is 15 m, then height is

(a) 10√3 m
(b) 15√3 m
(c) 20√3 m
(d) 25√3 m

Answer: (b)

Q50. Which statement is true?

(a) Angle of elevation is measured downward.
(b) Angle of depression is measured upward.
(c) Angle of elevation is measured above the horizontal line.
(d) Angle of elevation is always 90°.

Answer: (c) Angle of elevation is measured above the horizontal line.

Solution: It is the angle formed between the horizontal line and the upward line of sight.