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Sine Rule, Cosine Rule & Triangle Area (Year 11)

Free printable UK Year 11 (GCSE Higher tier) maths worksheet: use the sine rule, cosine rule and Area = 1/2 ab sin C in non-right-angled triangles, with accurate labelled diagrams.

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Grade 10 · Math worksheet
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Sine Rule, Cosine Rule & Triangle Area

These triangles are NOT right-angled, so SOHCAHTOA alone cannot solve them. Choose the sine rule (a pair of opposite side-angle pairs), the cosine rule (two sides and the included angle, or all three sides), or Area = 1/2 ab sin C. Round only your final answer, to 1 decimal place. Diagrams are drawn from the actual values but are not to measure from. Higher tier.

  1. 1.
    In triangle ABC, angle A = 76°, angle B = 67° and side a = 13 cm (the side opposite angle A). Use the sine rule to find side b, correct to 1 decimal place.
    ABC13 cmx cm76°67°
  2. 2.
    In triangle ABC, angle A = 49°, angle B = 79° and side a = 11 cm (the side opposite angle A). Use the sine rule to find side b, correct to 1 decimal place.
    ABC11 cmx cm49°79°
  3. 3.
    In triangle ABC, angle A = 66°, side a = 11 cm and side b = 8.1 cm. Use the sine rule to find the acute angle B (marked θ), correct to 1 decimal place.
    ABC11 cm8.1 cm66°θ
  4. 4.
    In triangle ABC, angle A = 68°, side a = 9 cm and side b = 7.3 cm. Use the sine rule to find the acute angle B (marked θ), correct to 1 decimal place.
    ABC9 cm7.3 cm68°θ
  5. 5.
    In triangle ABC, side b = 8 cm, side c = 9 cm and the angle between them is A = 59°. Use the cosine rule to find side a, correct to 1 decimal place.
    ABCx cm8 cm9 cm59°
  6. 6.
    In triangle ABC, side b = 5 cm, side c = 9 cm and the angle between them is A = 51°. Use the cosine rule to find side a, correct to 1 decimal place.
    ABCx cm5 cm9 cm51°
  7. 7.
    In triangle ABC, the three sides are a = 13.5 cm, b = 11 cm and c = 11 cm. Use the cosine rule to find angle A (marked θ), correct to 1 decimal place.
    ABC13.5 cm11 cm11 cmθ
  8. 8.
    In triangle ABC, the three sides are a = 7.8 cm, b = 6 cm and c = 9 cm. Use the cosine rule to find angle A (marked θ), correct to 1 decimal place.
    ABC7.8 cm6 cm9 cmθ
  9. 9.
    In triangle ABC, side a = 11 cm and side b = 6 cm meet at C, where angle C = 87°. Use Area = 12 ab sin C to find the area of the triangle, correct to 1 decimal place.
    ABC11 cm6 cm87°
  10. 10.
    In triangle ABC, side a = 13 cm and side b = 9 cm meet at C, where angle C = 70°. Use Area = 12 ab sin C to find the area of the triangle, correct to 1 decimal place.
    ABC13 cm9 cm70°
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