How to Find the Hypotenuse of a Triangle?

Step by step

1. Confirm it's a right triangle (one 90° angle). Pythagoras does not give the longest side of a non-right triangle.
2. Label the two sides that form the right angle as a and b. Label the side across from the 90° angle as c (hypotenuse — always the longest side).
3. Square a and b, add them, then take the square root to get c.

Worked example: legs 3 and 4.

• 3² + 4² = 9 + 16 = 25
• √25 = 5

So the hypotenuse is 5 (the familiar 3-4-5 triangle).

Another example: legs 5 and 12.

• 5² + 12² = 25 + 144 = 169
• √169 = 13

If you know the hypotenuse and one leg: rearrange to b = √(c² − a²). Example: hypotenuse 13, one leg 5 → other leg = √(169 − 25) = √144 = 12.

If it isn't a right triangle: you need a different tool — typically the law of cosines (c² = a² + b² − 2ab cos C) using the angle opposite the side you want — not a² + b² = c² by itself.

Quick identification: in a diagram, the hypotenuse is the side that doesn't touch the right-angle box; it's opposite that corner.

You may also want How to Find the Perimeter of a Triangle? or What Are Complementary Angles?.

Neighbouring how-tos sit on the Math & Study Help topic. From ask a follow-up you can ask a follow-up of your own — no account needed.