Which of these is a correct statement of the sine rule for a triangle with sides a, b, c opposite angles A, B, C?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Non-right-angled triangles Topical Past Papers.
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These Non-right-angled triangles Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Trigonometry (E6.5) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Apply the sine rule, cosine rule, and the triangle area formula ½ab sin C to non-right-angled triangles.
Which of these is a correct statement of the sine rule for a triangle with sides a, b, c opposite angles A, B, C?
In triangle ABC, A = 60°, B = 40° and the side a (opposite A) is 12 cm. Find the side b (opposite B), correct to 1 decimal place.
[1 mark]In triangle PQR, p = 8 cm, q = 11 cm and P = 35°. Find angle Q, correct to 1 decimal place.
[2 marks]In triangle ABC, b = 7 cm, c = 9 cm and A = 50°. Find side a using the cosine rule, correct to 1 decimal place.
[2 marks]Which rule should you use to find a side of a triangle given two other sides and the angle between them (the 'included' angle)?
In triangle XYZ, x = 14 cm, y = 12 cm and the angle between them (Z) is 65°.
Find the length of side z (opposite Z), correct to 1 decimal place.
[2 marks]Find the area of triangle XYZ, correct to 1 decimal place.
[1 mark]Triangle ABC has sides a = 7 cm, b = 10 cm and c = 13 cm. Find the size of angle B (opposite b), correct to 1 decimal place.
[2 marks]Triangle ABC has area 40 cm², side a = 10 cm and side b = 12 cm. Find the size of the included angle C, correct to 1 decimal place.
[2 marks]