4MA1/2HR Jan 2022, Question 16: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
Use area of triangle BCD and given side lengths to find angle ABD in quadrilateral ABCD, giving the answer to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Area of triangle BCD = ½ × 45 × 36 × sin C = 405
- 2sin C = (2 × 405) ÷ (45 × 36) = 810 ÷ 1620 = 0.5
- 3Angle BCD is acute, so C = 30°
- 4Cosine rule in triangle BCD: BD² = 45² + 36² − 2 × 45 × 36 × cos 30°
- 5BD² = 2025 + 1296 − 2805.92 = 515.08, so BD = 22.695 cm
- 6Cosine rule in triangle ABD: cos ABD = (AB² + BD² − AD²) ÷ (2 × AB × BD)
- 7cos ABD = (361 + 515.08 − 784) ÷ (2 × 19 × 22.695) = 92.08 ÷ 862.42 = 0.10677
- 8Angle ABD = 83.9° to 1 decimal place
Answer83.9
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