4024/22 May/Jun 2026, Question 22: The Sine Rule
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks
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The question, in short
Use the triangular garden diagram with CD = 8 m, angle ADC = 18°, angle ACB = 34° and right angle at B to work out triangle ABC's area, then the seed cost.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 6 marks
Calculate the area of triangle ABC in m², using CD = 8 m, angle ADC = 18°, angle ACB = 34° and the right angle at B.
- 1Angle ACD = 180 − 34 = 146°, angle CAD = 180 − 146 − 18 = 16°
- 2Sine rule: AC = 8 sin 18°/sin 16° = 8.968…
- 3AB = 8.968… × sin 34° = 5.015…
- 4BC = 8.968… × cos 34° = 7.435…
- 5Area = 1/2 × 5.015… × 7.435… = 18.6 m²
Answer18.6 to 18.7
Part (b) · 2 marks
Boxes cost $6 and each covers 5 m²; find the total cost of boxes needed for the area ABC.
- 118.6… ÷ 5 = 3.73…
- 2So 4 boxes are needed
- 34 × $6 = $24
Answer24
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