4MA1/1H Jun 2025, Question 20: 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 split by diagonal BD; triangle ABD has AB = 9.4 cm, AD = 12.8 cm and angle BAD = 72°, triangle BCD has angle BCD = 54° and angle BDC = 39°. Find BC to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1BD² = 9.4² + 12.8² − 2 × 9.4 × 12.8 × cos 72°
- 2BD² = 177.8…, BD = 13.33…
- 3BC/sin 39° = BD/sin 54°
- 4BC = 13.33… × sin 39° ÷ sin 54°
- 5BC = 10.37… = 10.4 (3 s.f.)
Answer10.4
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