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Use the Pythagorean theorem
For a right triangle, the side lengths satisfy a² + b² = c², where c is the hypotenuse opposite the right angle.
a² + b² = c²
Worked example
If the legs are 6 and 8, then c² = 36 + 64 = 100, so c = 10.
Finding a leg instead of the hypotenuse
If the hypotenuse and one leg are known, rearrange the formula: a = √(c² − b²).
Common mistakes
- Using the formula on a triangle that is not right.
- Forgetting to take the square root at the end.
- Treating the hypotenuse as one of the shorter legs.
Frequently asked questions
Which side is c?
c is the hypotenuse, the side opposite the 90° angle.
Can I find a leg with the same formula?
Yes. Subtract the known leg squared from the hypotenuse squared, then take the square root.
What if I know angles instead of two sides?
Use right-triangle trigonometry such as sine, cosine or tangent.