4MA1/1HR Jan 2023, Question 17: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Triangle ABC has AB = 4.6 cm, BC = 8.3 cm, acute angle ABC, and area 12 cm². Work out the perimeter, giving the answer to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Area: ½ × 4.6 × 8.3 × sin B = 12
- 2sin B = 24 ÷ 38.18 = 0.6286; B is acute, so B = 38.95°
- 3Cosine rule: AC² = 4.6² + 8.3² − 2 × 4.6 × 8.3 × cos 38.95° = 30.66
- 4AC = √30.66 = 5.537 cm
- 5Perimeter = 4.6 + 8.3 + 5.537 = 18.437 = 18.4
Answer18.4
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