IGCSE Math RevisionQuestion 1
The two shorter sides of a right-angled triangle are \(9\) cm and \(12\) cm.
Find the length of the hypotenuse.
Show the worked answer
- \(h^2 = 9^2 + 12^2 = 81 + 144 = 225\)
- \(h = \sqrt{225} = 15\) cm
Answer: \(15\) cm
Cambridge IGCSE Maths (0580) · Topic 6: Trigonometry · 6.1
Cambridge IGCSE Maths 0580 Pythagoras' Theorem Questions
Pythagoras' Theorem questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 10 questions
- 10 Core
- 2 non-calculator
- Free, no sign-in
What the syllabus asks
- 6.1 Pythagoras' theorem Core
Know and use Pythagoras' theorem in two dimensions.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Pythagoras' Theorem questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
The longest side of a right-angled triangle is \(25\) cm and one of the shorter sides is \(7\) cm.
Work out the length of the remaining side.
Show the worked answer
- \(a^2 = 25^2 - 7^2 = 625 - 49 = 576\)
- \(a = 24\) cm
Answer: \(24\) cm
Question 3
The two shorter sides of a right-angled triangle are 4.5 cm and 7 cm. Find the length of the hypotenuse. Give your answer correct to 3 significant figures.
Show the answer and mark scheme
- M1 √(4.5² + 7²)
- A1 8.32 cm (8.321…)
Answer: \(8.32\) cm
Question 4
The two shorter sides of a right-angled triangle are \(7\) cm and \(10\) cm.
Find the hypotenuse, correct to 3 significant figures.
Show the worked answer
- \(h^2 = 49 + 100 = 149\)
- \(h = \sqrt{149} = 12.20\ldots\) cm
Answer: \(12.2\) cm
Question 5
The top of a \(5\) m ladder rests against a vertical wall, with its base on flat ground \(1.4\) m out from the wall.
Work out the height of the top of the ladder above the ground.
Show the worked answer
- \(h^2 = 5^2 - 1.4^2 = 25 - 1.96 = 23.04\)
- \(h = \sqrt{23.04} = 4.8\) m
Answer: \(4.8\) m
Question 6
A rectangle is \(15\) cm long and \(8\) cm wide.
Find the length of its diagonal.
Show the worked answer
- \(d^2 = 15^2 + 8^2 = 225 + 64 = 289\)
- \(d = 17\) cm
Answer: \(17\) cm
Question 7
A triangle has sides \(8\) cm, \(15\) cm and \(17\) cm.
Is it a right-angled triangle? Show how you decide.
Show the worked answer
- \(8^2 + 15^2 = 64 + 225 = 289\) and \(17^2 = 289\).
- The squares of the two shorter sides add to the square of the longest, so it is right-angled.
Answer: Yes, because \(8^2 + 15^2 = 17^2\)
Question 8
A triangle has sides 9 cm, 12 cm and 15 cm. Show that it is a right-angled triangle.
Show the answer and mark scheme
- M1 9² + 12² = 81 + 144
- A1 = 225 = 15², so right-angled
Answer: \(9^2 + 12^2 = 225 = 15^2\), so it is right-angled
Question 9
A ladder 6 m long leans against a vertical wall. Its foot is 1.8 m from the wall. How high up the wall does the ladder reach? Give your answer correct to 3 significant figures.
Show the answer and mark scheme
- M1 √(6² − 1.8²)
- A1 5.72 m (5.723…)
Answer: \(5.72\) m
Question 10
An isosceles triangle has two sides of \(10\) cm and a base of \(12\) cm.
Work out its area.
Show the worked answer
- The height splits the base into \(6\) cm and \(6\) cm.
- Height \(= \sqrt{10^2 - 6^2} = \sqrt{64} = 8\) cm.
- Area \(= \frac{1}{2} \times 12 \times 8 = 48\) cm²
Answer: \(48\) cm²
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Trigonometry practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Trigonometry revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test Pythagoras' theorem?
Pythagoras' Theorem is on both tiers (syllabus 6.1), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more Pythagoras' theorem questions?
In the 0580 practice for topic 6 (Trigonometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.