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Rearrange the Pythagorean theorem
Start with a² + b² = c². To find a missing leg, subtract the known leg squared from the hypotenuse squared.
a = √(c² − b²)
Worked example
If c = 13 and b = 5, then a = √(169 − 25) = √144 = 12.
Check the result
A leg must be shorter than the hypotenuse. Substituting the values back into a² + b² = c² confirms the result.
Common mistakes
- Subtracting c² from the leg squared instead of the other way around.
- Using a negative value under the square root.
- Forgetting the square root.
Frequently asked questions
Can a leg be longer than the hypotenuse?
No. The hypotenuse is always the longest side of a right triangle.
What if c² − b² is negative?
That means the supplied lengths cannot form a right triangle with c as the hypotenuse.
How do I verify the answer?
Square both legs and confirm their sum equals the hypotenuse squared.