4MA1/1H Jan 2019, Question 17: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Triangle ABC has AB = 4.1 cm, BC = 5.3 cm and angle ABC = 110°. Calculate angle BAC, labelled x, 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
- 1Cosine rule: AC² = 4.1² + 5.3² − 2 × 4.1 × 5.3 × cos 110°
- 2AC² = 16.81 + 28.09 + 14.864… = 59.764…, so AC = 7.7307…
- 3Sine rule: sin x/5.3 = sin 110°/7.7307…
- 4sin x = 5.3 × sin 110° ÷ 7.7307… = 0.6442…
- 5x = sin⁻¹(0.6442…) = 40.1
Answer40.1
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