4PM1/02R Jan 2020, Question 3: Area of a Triangle Using Sine
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 5 marks
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The question, in short
Triangle ABC has AB = 11 cm, BC = 12 cm and area 33 cm². Find both possible lengths of AC in cm to 3 significant figures.
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Solution · 5 marks
- 1½ × 11 × 12 × sin B = 33, so sin B = 1/2
- 2B = 30° or 150°
- 3AC² = 11² + 12² − 2 × 11 × 12 cos 30° gives AC = 6.03 cm
- 4AC² = 11² + 12² − 2 × 11 × 12 cos 150° gives AC = 22.2 cm
AnswerAC = 6.03 cm or 22.2 cm
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