4MA1/2H Jun 2021, Question 18: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
Cyclic quadrilateral ABCD has AB = 8 cm, BC = 7.5 cm, angle ABC = 98° and angle ACD = 35°. Find its perimeter, correct to one decimal place.
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Solution · 6 marks
- 1Cosine rule: AC² = 8² + 7.5² − 2 × 8 × 7.5 × cos 98° = 136.95…, so AC = 11.70…
- 2Opposite angles of a cyclic quadrilateral add to 180°: angle ADC = 180 − 98 = 82°
- 3Angle CAD = 180 − 82 − 35 = 63°
- 4Sine rule: CD = 11.70… × sin 63° ÷ sin 82° = 10.53…; AD = 11.70… × sin 35° ÷ sin 82° = 6.78…
- 5Perimeter = 8 + 7.5 + 10.53… + 6.78… = 32.8
Answer32.8
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