0580/23 Oct/Nov 2025, Question 10: Pythagoras' Theorem
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks
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The question, in short
Right-angled triangle ABC has the right angle at A, with AB = 8 cm and BC = 11 cm. Find the exact length of AC and the value of k where cos x = k.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Calculate the exact length of side AC in the right-angled triangle with AB = 8 cm and BC = 11 cm.
- 1BC is the hypotenuse: 11² = AC² + 8²
- 2AC² = 121 − 64 = 57
- 3AC = √57 cm
Answer√57
Part (b) · 1 mark
Given cos x = k, state the value of k for angle x at B.
- 1cos x = adjacent/hypotenuse = AB/BC
- 2k = 8/11
Answer8/11
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