Lesson G22

G22 Sine rule and cosine rule Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G22, Sine rule and cosine rule: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. (H) Which expression is the sine rule for triangle ABC?

    • a/cos A = b/cos B = c/cos C
    • a/sin B = b/sin C = c/sin A
    • a + b + c = sin A + sin B + sin C
    • a/sin A = b/sin B = c/sin C

  2. (H) Which expression is the cosine rule for finding side a in triangle ABC?

    • a^2 = b^2 + c^2 + 2bc cos A
    • a^2 = b^2 + c^2 - 2bc cos A
    • a^2 = b^2 - c^2 + 2bc cos A
    • a = b + c - 2bc sin A

  3. (H) In triangle ABC, angle A = 40 degrees, angle B = 70 degrees and side a = 8 cm. What is side b, to 1 decimal place?

    • 5.5 cm
    • 8.0 cm
    • 11.7 cm
    • 12.9 cm

  4. (H) In triangle ABC, b = 5 cm, c = 7 cm and angle A = 60 degrees. What is side a, to 1 decimal place?

    • 4.5 cm
    • 8.9 cm
    • 12.0 cm
    • 6.2 cm

  5. (H) Two sides of a triangle and the angle between them are known. Which rule is needed to find the third side?

    • The tangent ratio
    • Pythagoras' theorem only
    • The sine rule
    • The cosine rule

  6. (H) In triangle ABC, a = 7 cm, b = 5 cm and c = 6 cm. What is angle A, to the nearest degree?

    • 58 degrees
    • 78 degrees
    • 102 degrees
    • 36 degrees

  7. (H) In triangle ABC, a = 9 cm, b = 4 cm and c = 6 cm. What is angle A, to the nearest degree?

    • 127 degrees
    • 97 degrees
    • 53 degrees
    • 117 degrees

  8. (H) In triangle PQR, p = 10 cm, angle Q = 30 degrees and angle R = 80 degrees. What is side q, to 1 decimal place?

    • 9.8 cm
    • 5.3 cm
    • 10.6 cm
    • 4.7 cm

  9. (H) In triangle XYZ, angle X = 50 degrees, angle Y = 35 degrees and side y = 12 cm. What is side x, to 1 decimal place?

    • 22.5 cm
    • 16.0 cm
    • 9.2 cm
    • 8.3 cm

  10. (H) Two sides of a triangle are 6 cm and 8 cm, with an included angle of 60 degrees. What is the third side, to 1 decimal place?

    • 10.0 cm
    • 14.0 cm
    • 8.7 cm
    • 7.2 cm

  11. (H) In triangle DEF, d = 7 cm, e = 9 cm and f = 10 cm. What is angle D, to the nearest degree?

    • 43 degrees
    • 58 degrees
    • 47 degrees
    • 75 degrees

  12. (H) In triangle ABC, a = 10 cm, b = 8 cm and angle A = 35 degrees. What is angle B, to the nearest degree?

    • 153 degrees
    • 63 degrees
    • 35 degrees
    • 27 degrees

  13. (H) In triangle ABC, a = 4 cm, b = 6 cm and angle C = 120 degrees. What is side c, to 1 decimal place?

    • 6.9 cm
    • 8.7 cm
    • 4.5 cm
    • 10.0 cm

  14. (H) In triangle ABC, a = 5 cm, b = 7 cm and c = 9 cm. What is angle C, to the nearest degree?

    • 96 degrees
    • 54 degrees
    • 70 degrees
    • 42 degrees

  15. (H) In triangle ABC, a = 12 cm, angle A = 40 degrees and angle B = 60 degrees. What is side b, to 1 decimal place?

    • 14.1 cm
    • 16.2 cm
    • 18.7 cm
    • 7.5 cm

  16. (H) Two sides of a triangle are 5 cm and 8 cm, with an included angle of 100 degrees. What is the third side, to 1 decimal place?

    • 6.1 cm
    • 8.7 cm
    • 13.0 cm
    • 10.1 cm

  17. (H) A triangle has sides a = 4 cm, b = 5 cm and c = 6 cm. What is cos B?

    • 0.4375
    • 0.6667
    • 0.5625
    • 0.3125

  18. (H) In a triangle, a^2 is greater than b^2 + c^2. What can you say about angle A?

    • Angle A is acute
    • Angle A is obtuse
    • Angle A is 45 degrees
    • Angle A is a right angle

  19. (H) A triangle has sides 7 cm, 8 cm and 9 cm. Which angle is the largest?

    • The angle opposite 7 cm
    • The angle opposite 9 cm
    • All three are equal
    • The angle opposite 8 cm

  20. (H) Given a, b and angle A with a less than b sin A, how many triangles can be formed?

    • Infinitely many
    • One
    • None
    • Two

All AQA Maths quizzes