4MA1/1HR Jan 2020, Question 21: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
Use the triangular prism with AC = 6 cm, CE = 13 cm, angle BEC = 40° and triangle ABC area 22 cm² to calculate AB to one decimal place.
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Solution · 6 marks
- 1Triangle BCE is right-angled at B: BC = 13 × sin 40° = 8.356…
- 2½ × 6 × 8.356… × sin C = 22, so sin C = 0.8775…
- 3C is obtuse: C = 180 − 61.35 = 118.65°
- 4AB² = 6² + 8.356…² − 2 × 6 × 8.356… × cos 118.65° = 153.98…
- 5AB = √153.98… = 12.4
Answer12.4
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