4MA1/2H Jan 2022, Question 23: The Ambiguous Case of the Sine Rule
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
Triangle PQR has PQ = 1.6 cm, PR = 4.2 cm and angle PRQ = 18°, with angle PQR obtuse. Find the area of the triangle to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1sin Q / 4.2 = sin 18 / 1.6
- 2sin Q = (4.2 × sin 18) / 1.6
- 3sin Q = 0.811...
- 4Q = sin⁻¹(0.811...) = 54.2°
- 5Since angle PQR is obtuse, Q = 180 − 54.2 = 125.8°
- 6Angle at P = 180 − 125.8 − 18 = 36.2°
- 7Area = (1/2) × 4.2 × 1.6 × sin(36.2)
- 8Area = 0.5 × 4.2 × 1.6 × 0.590
- 9Area = 1.98
Answer1.98
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