4MA1/1HR Jun 2018, Question 18: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
Quadrilateral PQRS split by diagonal SQ: use the cosine rule in triangle PQS (12 cm, 8 cm, 120°), then the sine rule to find angle SQR.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Cosine rule: SQ² = 8² + 12² − 2 × 8 × 12 × cos 120°
- 2SQ² = 304, so SQ = 17.436…
- 3Sine rule: sin SRQ = 17.436… × sin 27° ÷ 9 = 0.8795…
- 4SRQ is acute, so SRQ = 61.58…°
- 5SQR = 180 − 27 − 61.58… = 91.4°
Answer91.4
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