Pythagoras Question Generator

What this generator does

Generates right-angled triangle questions with one side missing. At the gentle level the sides come from a Pythagorean triple multiplied up, so the answer is a whole number. Above that the legs are drawn freely and the answer is given to two decimal places.

How to use this tool

1. Choose how many questions you want and at what level.
2. Work out the missing side, deciding first whether you are adding or subtracting squares.
3. Reveal the answers, and the working if you want the squares written out.
4. Seed the set to hand the same questions to someone else.

Understanding the controls

How many questions

Between 1 and 20. Twelve makes a full practice set with both directions represented.

Level

Gentle uses triples only and always asks for the hypotenuse. Standard and stretch draw sides freely and mix in find-the-leg questions with larger numbers.

Seed

The same word gives the same triangles, so a set can be reissued or printed twice identically.

Show the answers / working

The missing side, or the squares and the square root written out step by step.

Common use cases

• Practice where the arithmetic stays whole while the method is being learned
• Mixing find-the-hypotenuse and find-a-leg questions in one set
• Showing why the hypotenuse question adds and the leg question subtracts
• Introducing Pythagorean triples as a family rather than as three memorised numbers
• Producing a printable set for a class from a shared seed

How this generator works

Triple-based questions multiply one of six primitive triples by a small factor, so a² + b² = c² holds exactly. Free questions compute the missing side by square root and round to two places. The check recomputes the side from the two given lengths, rounds it the same way, and requires a match — and it rejects any find-a-leg question where the stated hypotenuse is not the longest side.

Randomness and fairness

Which triangle you get is random. Whether the answer is exact is a property of how the question was built, and is stated rather than left to chance. Seeded sets are reproducible and therefore explicitly not cryptographically secure; unseeded ones use the browser's cryptographically secure generator.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• Only right-angled triangles. The cosine rule case, where there is no right angle, is not covered.
• Answers are lengths in centimetres; the questions are not dressed up as real-world scenarios.
• Three-dimensional Pythagoras, where the theorem is applied twice, is not among the question types.
• Nothing is marked — the answer is revealed for comparison.
• Sets are not stored between visits, so seed anything you want to print.

Privacy and your data

Triangles are generated in your browser. Your seed, level and the questions themselves never leave the page.