A right-angled triangle has shorter sides of length 3 cm and 4 cm. Find the hypotenuse.
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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 Pythagoras' theorem Topical Past Papers.
Top questions students ask on this sub-topic
These Pythagoras' theorem Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Trigonometry (E6.1) 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 Pythagoras' theorem in 2-D right-angled triangles to find unknown sides.
A right-angled triangle has shorter sides of length 3 cm and 4 cm. Find the hypotenuse.
Find the hypotenuse of a right-angled triangle with shorter sides 6 cm and 8 cm.
[1 mark]A right-angled triangle has hypotenuse 17 cm and one shorter side 15 cm. Find the length of the other shorter side.
[2 marks]Find the exact length of the hypotenuse of a right-angled triangle with shorter sides 5 cm and 4 cm. Give your answer in surd form.
[2 marks]Which set of three lengths forms a Pythagorean triple (a right-angled triangle)?
A ladder of length 5 m leans against a vertical wall. The base of the ladder is 1.4 m from the foot of the wall.
Find the height up the wall the ladder reaches. Give your answer correct to 2 decimal places.
[2 marks]The base of the ladder is moved 0.4 m further from the wall. By how much, in metres, does the top of the ladder drop down the wall? Give your answer correct to 2 dp.
[1 mark]A right-angled triangle has hypotenuse 13 cm. One of the shorter sides is 5 cm longer than the other. Find the lengths of the two shorter sides.
[2 marks]An isosceles triangle has two equal sides of length 10 cm and a base of length 12 cm. Find the perpendicular height of the triangle from the base to the apex.
[2 marks]