Sine Rule, Cosine Rule & Triangle Area (Year 10)
Free printable UK Year 10 (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 9 · 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.In triangle ABC, angle A = 78°, angle B = 64° and side a = 8 cm (the side opposite angle A). Use the sine rule to find side b, correct to 1 decimal place.
- 2.In triangle ABC, angle A = 65°, angle B = 45° and side a = 7 cm (the side opposite angle A). Use the sine rule to find side b, correct to 1 decimal place.
- 3.In triangle ABC, angle A = 70°, side a = 13 cm and side b = 10.1 cm. Use the sine rule to find the acute angle B (marked θ), correct to 1 decimal place.
- 4.In triangle ABC, angle A = 61°, side a = 13 cm and side b = 9.2 cm. Use the sine rule to find the acute angle B (marked θ), correct to 1 decimal place.
- 5.In triangle ABC, side b = 5 cm, side c = 7 cm and the angle between them is A = 59°. Use the cosine rule to find side a, correct to 1 decimal place.
- 6.In triangle ABC, side b = 11 cm, side c = 11 cm and the angle between them is A = 100°. Use the cosine rule to find side a, correct to 1 decimal place.
- 7.In triangle ABC, the three sides are a = 9.7 cm, b = 6 cm and c = 7 cm. Use the cosine rule to find angle A (marked θ), correct to 1 decimal place.
- 8.In triangle ABC, the three sides are a = 11.5 cm, b = 9 cm and c = 8 cm. Use the cosine rule to find angle A (marked θ), correct to 1 decimal place.
- 9.In triangle ABC, side a = 6 cm and side b = 10 cm meet at C, where angle C = 57°. Use Area = 12 ab sin C to find the area of the triangle, correct to 1 decimal place.
- 10.In triangle ABC, side a = 10 cm and side b = 12 cm meet at C, where angle C = 46°. Use Area = 12 ab sin C to find the area of the triangle, correct to 1 decimal place.
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