4PM1/01R Jun 2025, Question 4: The Ambiguous Case of the Sine Rule
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks
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The question, in short
Triangle ABC has AB = 4.3 cm, BC = 5.9 cm and angle BCA = 29°. Find two possible values of angle CAB, then the shortest possible length of AC.
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Part (a) · 4 marks
Use the given sides and angle BCA = 29° to find both possible values of angle CAB in degrees, to one decimal place.
- 1sin A/5.9 = sin 29°/4.3
- 2sin A = 5.9 sin 29°/4.3 = 0.66520…
- 3A = 41.7°
- 4or A = 180° − 41.7° = 138.3°
Answer41.7° and 138.3°
Part (b) · 3 marks
Using the smaller angle CAB, calculate the shortest possible length of AC in cm, to 3 significant figures.
- 1Use the obtuse angle: angle B = 180° − (29° + 138.3°) = 12.698…°
- 2AC² = 5.9² + 4.3² − 2 × 5.9 × 4.3 × cos 12.698…°
- 3AC = 1.95 cm
AnswerAC = 1.95 cm
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