Pythagoras Theorem: When to Use It (and When You're Wasting Time)
May 8, 2026 · 4 min · pythagoras · geometry · math
a² + b² = c² is the most famous formula in school. It's also misused.
When it applies
Only when you have a right-angled triangle, and you know two of the three sides.
If the triangle is not right-angled, Pythagoras doesn't work. Use the cosine rule instead.
The trigger phrase
When you spot a right-angle marker (a small square in the corner) and you need a missing side, that is your moment.
The two directions
- Find the hypotenuse: a² + b² = c² → c = √(a² + b²)
- Find a leg: c² - b² = a² → a = √(c² - b²)
The hypotenuse is always the longest side, opposite the right angle.
Where students lose marks
- Plugging the hypotenuse where a or b should go. Always check: hypotenuse must be c.
- Forgetting the square root.
- Using it on a non-right triangle.
Three-dimensional version
If you have a cuboid and need the diagonal, use Pythagoras twice. Find the diagonal of the base first, then use that with the height.
Pythagorean triples worth memorising
3-4-5, 5-12-13, 8-15-17, 7-24-25. If you see any of these as two sides, the third is the same triple. Saves you the calculation.