0580/43 Oct/Nov 2025, Question 18: The Sine Rule
Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 6 marks
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The question, in short
Using the diagram of a quadrilateral divided by a 64.5 cm diagonal, calculate the angles x and y from the given side lengths and 102° angle.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
In the upper triangle with sides 41.3 cm and 64.5 cm and an included angle of 102°, calculate x.
- 1Sine rule: sin x/41.3 = sin 102/64.5
- 2sin x = 41.3 × sin 102 ÷ 64.5 = 0.6263…
- 3x = 38.8
Answer38.8 or 38.77 to 38.78
Part (b) · 3 marks
In the lower triangle with sides 64.5 cm, 52.1 cm and 70.2 cm, calculate the angle y.
- 1Cosine rule: cos y = (64.5² + 52.1² − 70.2²)/(2 × 64.5 × 52.1)
- 2= 1946.62 ÷ 6720.9 = 0.2896…
- 3y = 73.2
Answer73.2 or 73.16…
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