4MA1/1HR Jun 2019, Question 25: Bearings with Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
A boat travels X to Y (3.5 km) then Y to Z (6 km), with given bearings at X and Y; find the bearing of Z from X to 1 decimal place.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Bearing of X from Y is 280° − 180° = 100°, so angle XYZ = 220° − 100° = 120°
- 2Cosine rule: XZ² = 3.5² + 6² − 2 × 3.5 × 6 × cos 120° = 69.25, so XZ = 8.32 km
- 3Sine rule: sin YXZ = 6 × sin 120° ÷ 8.32 = 0.624, so angle YXZ = 38.6°
- 4Bearing of Z from X = 280° − 38.6° = 241.4
Answer241.4
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