4MA1/1HR Jun 2022, 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
Parallelogram PQRS has PQ = 6.1 cm, PS = 3.8 cm and area 18 cm², with angle SPQ acute. Find the diagonal QS, giving the answer to 3 significant figures.
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Solution · 5 marks
- 1Area = 6.1 × 3.8 × sin P = 18, so sin P = 18 ÷ 23.18 = 0.7765
- 2Angle SPQ is acute, so P = 50.93°
- 3Cosine rule: QS² = 6.1² + 3.8² − 2 × 6.1 × 3.8 × cos 50.93°
- 4QS² = 51.65 − 29.22 = 22.43
- 5QS = √22.43 = 4.74
Answer4.74
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