In a right-angled triangle, which ratio equals sin(θ)?
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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 Right-angled triangles Topical Past Papers.
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These 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 (E6.2) 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.
Use sine, cosine and tangent in right-angled triangles to find sides and angles.
In a right-angled triangle, which ratio equals sin(θ)?
In a right-angled triangle, the angle θ has opposite side of length 7 cm and hypotenuse of length 14 cm. Find the value of sin(θ).
[1 mark]A right-angled triangle has hypotenuse 20 cm and an angle of 35°. Find the length of the side OPPOSITE to the 35° angle, correct to 1 decimal place.
[2 marks]In a right-angled triangle, the opposite side is 8 cm and the adjacent side is 6 cm (relative to angle θ). Find angle θ, correct to 1 decimal place.
[2 marks]A right-angled triangle has an angle of 50°. You know the hypotenuse and want to find the adjacent side. Which trigonometric ratio should you use?
A right-angled triangle has hypotenuse 25 cm and a known angle of 28°.
Find the length of the side opposite the 28° angle, correct to 1 decimal place.
[1 mark]Find the length of the side adjacent to the 28° angle, correct to 1 decimal place.
[2 marks]A surveyor stands 50 m from the base of a vertical tower. The angle of elevation from the surveyor to the top of the tower is 38°. Find the height of the tower, correct to 1 decimal place.
[2 marks]From a point P at sea level, the angle of elevation to the top of a cliff is 25°. From a point Q, 80 m closer to the base of the cliff (along the same horizontal line), the angle of elevation is 40°. Find the height of the cliff, correct to 1 decimal place.
[2 marks]