4MA1/1H Jun 2024, Question 19: 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
Quadrilateral ABCD with diagonal BD has AB = 15.2 m, AD = 13.4 m, BC = 12.8 m, angle BDC = 40°, angle BCD = 62°. Find x, the angle DAB, to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Triangle BCD, sine rule: BD/sin 62° = 12.8/sin 40°.
- 2BD = 12.8 × sin 62° ÷ sin 40° = 17.58 m.
- 3Triangle ABD, cosine rule: cos x = (13.4² + 15.2² − BD²) ÷ (2 × 13.4 × 15.2).
- 4cos x = (179.56 + 231.04 − 309.14) ÷ 407.36 = 0.2491.
- 5x = cos⁻¹(0.2491) = 75.6
Answer75.6
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