4PM1/02 Jun 2019, Question 4: The Cosine Rule
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks
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The question, in short
Use the cosine rule in triangle ABC with sides 5x, 3x − 1, 2x + 5 cm and angle 60° at B to find x to 3 significant figures.
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Solution · 5 marks
- 1Cosine rule: (2x + 5)² = (3x − 1)² + (5x)² − 2(3x − 1)(5x) cos 60°
- 24x² + 20x + 25 = 9x² − 6x + 1 + 25x² − 15x² + 5x
- 315x² − 21x − 24 = 0 (5x² − 7x − 8 = 0)
- 4x = (21 ± √(21² + 4 × 15 × 24))/30
- 5x = 2.1456… (reject −0.7456…), so x = 2.15
Answerx = 2.15
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