10 Maths Chapter 8 MCQs – Projection of a Side of a Triangle (FBISE)

By tmagriou / May 9, 2026

Description: Practice Class 10 Maths Chapter 8 MCQs on Projection of a Side of a Triangle. These important questions are based on FBISE exam pattern and include trigonometric applications and cosine rule.

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1. Projection of a side of a triangle depends on:

A) Area
B) Cosine of angle
C) Sine of angle
D) Tangent

2. The projection of side $b$ on side $a$ is given by:

A) $b \cos C$
B) $b \sin C$
C) $a \cos B$
D) $a \sin B$

3. The projection formula is derived using:

A) Pythagoras theorem
B) Sine rule
C) Cosine rule
D) Area formula

4. In triangle ABC, projection of side $c$ on $b$ is:

A) $c \sin A$
B) $b \cos C$
C) $a \cos B$
D) $c \cos A$

5. If angle is $90^\circ$ , projection becomes:

A) Maximum
B) Zero
C) Negative
D) Infinite

6. If angle is $0^\circ$ , projection is:

A) Equal to the side
B) Zero
C) Negative
D) Undefined

7. Projection is maximum when angle is:

A) $90^\circ$
B) $60^\circ$
C) $0^\circ$
D) $45^\circ$

8. Projection is zero when angle is:

A) $0^\circ$
B) $30^\circ$
C) $60^\circ$
D) $90^\circ$

9. In triangle, projection involves:

A) Adjacent side
B) Opposite side
C) Hypotenuse only
D) Area

10. Cosine rule is written as:

A) $a^2 = b^2 + c^2$
B) $a^2 = b^2 + c^2 - 2bc \cos A$
C) $a = b + c$
D) $a^2 = bc$

11. Projection of side $a$ on $b$ is:

A) $a \sin C$
B) $b \cos A$
C) $a \cos C$
D) $c \cos B$

12. If angle is obtuse, projection is:

A) Negative
B) Positive
C) Zero
D) Undefined

13. If angle is acute, projection is:

A) Zero
B) Negative
C) Infinite
D) Positive

14. Projection is related to:

A) tan
B) cos
C) sin
D) cot

15. In triangle ABC, $a = 5, b = 4, C = 60^\circ$ , projection of $a$ on $b$ is:

A) 2
B) 3
C) $5 \cos 60^\circ$
D) 4

16. $\cos 0^\circ =$

A) 1
B) 0
C) -1
D) √3

17. $\cos 90^\circ =$

A) 1
B) -1
C) √3
D) 0

18. Using cosine rule, $a^2 = b^2 + c^2 - 2bc \cos A$ . If $A = 90^\circ$ , then:

A) $a^2 = b^2 - c^2$
B) $a^2 = b^2 + c^2$
C) $a = b + c$
D) $a = bc$

19. If $a = 5, b = 6, C = 60^\circ$ , then $c^2 =$

A) 25 + 36
B) 25 + 36 – 60
C) $25 + 36 - 2(5)(6)\cos 60^\circ$
D) $5 + 6$

20. $\cos 60^\circ =$

A) 1/2
B) √3/2
C) 1
D) 0

21. If projection is negative, angle is:

A) Acute
B) Right
C) Zero
D) Obtuse

22. If projection of $b$ on $a$ is zero, then angle between them is:

A) $0^\circ$
B) $90^\circ$
C) $60^\circ$
D) $30^\circ$

23. If $\cos \theta = -1$ , then $\theta =$

A) $0^\circ$
B) $90^\circ$
C) $180^\circ$
D) $60^\circ$

24. If $a = 3, b = 4, C = 90^\circ$ , then $c =$

A) 5
B) 7
C) 6
D) 1

25. Projection formula helps to find:

A) Area
B) Perimeter
C) Height
D) Component of a side

26. If $a = 7, b = 5, C = 0^\circ$ , then $c =$

A) 2
B) 2
C) 12
D) 35

27. If $C = 180^\circ$ , then $\cos C =$

A) 1
B) 0
C) -1
D) √3

28. Projection of $a$ on $b$ is maximum when:

A) Angle = $0^\circ$
B) Angle = $90^\circ$
C) Angle = $60^\circ$
D) Angle = $45^\circ$

29. Projection of a vector-like quantity is related to:

A) sin
B) tan
C) cot
D) cos

30. If $a = b$ and angle between them is $60^\circ$ , then projection is:

A) $a$
B) $a \cos 60^\circ$
C) $a \sin 60^\circ$
D) 0

31. Which identity is used in projection problems?

A) $\sin^2\theta + \cos^2\theta$
B) $1 + \tan^2\theta$
C) Cosine rule
D) Sine rule

32. If angle is acute, cosine value is:

A) Positive
B) Negative
C) Zero
D) Undefined

33. If angle is obtuse, cosine value is:

A) Positive
B) Zero
C) Infinite
D) Negative

34. Projection is useful in:

A) Algebra
B) Geometry
C) Arithmetic
D) Statistics

35. If $a = 6, b = 8, C = 90^\circ$ , then $c =$

A) 10
B) 12
C) 14
D) 8

36. If projection of a side is zero, triangle is:

A) Acute angled
B) Obtuse angled
C) Right angled
D) Equilateral

37. If $a = 10, b = 10, C = 60^\circ$ , then projection of $a$ on $b$ is:

A) 10
B) $10 \cos 60^\circ$
C) 5
D) 0

38. If angle between two sides increases, projection:

A) Increases
B) Remains same
C) Doubles
D) Decreases

39. If $\cos \theta = 0$ , projection is:

A) Zero
B) Maximum
C) Negative
D) Undefined

40. If $a = 5, b = 12, C = 90^\circ$ , then $c =$

A) 17
B) 10
C) 13
D) 7

41. Projection is minimum when angle is:

A) $0^\circ$
B) $180^\circ$
C) $60^\circ$
D) $45^\circ$

42. If $\cos \theta = 1$ , then projection is:

A) Zero
B) Negative
C) Minimum
D) Maximum

43. If $\cos \theta = -1$ , projection is:

A) Maximum negative
B) Zero
C) Positive
D) Undefined

44. Projection depends on:

A) Sine
B) Tangent
C) Cosine
D) Cotangent

45. If sides are perpendicular, projection is:

A) Maximum
B) Zero
C) Negative
D) Infinite

46. If sides are parallel, projection is:

A) Equal to side
B) Zero
C) Negative
D) Undefined

47. In cosine rule, term $-2bc \cos A$ represents:

A) Area
B) Perimeter
C) Height
D) Projection effect

48. If $a^2 = b^2 + c^2$ , then angle A is:

A) Acute
B) Right angle
C) Obtuse
D) Straight

49. If $a^2 > b^2 + c^2$ , then angle A is:

A) Acute
B) Right
C) Obtuse
D) Zero

50. If $a^2 < b^2 + c^2$ , then angle A is:

A) Acute
B) Right
C) Obtuse
D) Straight

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