0580/13 May/Jun 2022, Question 17: The Cosine Ratio
Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 3 marks
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The question, in short
Two right-angled triangles ABC and PQR are shown with AB = PQ = 7.3 cm and BC = QR = 9.2 cm; complete a similarity statement and find angle ABC.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 1 mark
Complete the statement naming the geometrical relationship between triangle ABC and triangle PQR.
- 1Both have a right angle, hypotenuse 9.2 cm and side 7.3 cm (RHS), so triangle ABC is congruent to triangle PQR
AnswerCongruent
Part (b) · 2 marks
Calculate angle ABC using the given side lengths 7.3 cm and 9.2 cm.
- 1cos ABC = 7.3/9.2
- 2ABC = cos⁻¹(7.3/9.2)
- 3= 37.48… ≈ 37.5°
Answer37.5 or 37.48 to 37.49
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Also searched as: 0580/13/M/J/22 · 0580_s22_qp_13 · 0580 s22 13 · question 17.
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