Pythagorean Theorem Examples

a² + b² = c²

These examples show how to substitute values, square, and solve for the hypotenuse.

Pick any right triangle, plug in the two known sides, and follow the formula to get the missing length.

Example 1

Classic 3-4-5

A right triangle with legs 3 and 4 has hypotenuse 5.

3² + 4² = 5²

Example 2

Solve for c

If a = 6 and b = 8, then c = 10.

6² + 8² = 10²

Example 3

Missing leg

If c = 13 and a = 5, then b = 12.

5² + 12² = 13²

✓Step-by-step example

Insert values

3² + 4² = c²

Square each side

9 + 16 = c²

Add them

25 = c²

Take the square root

c = √25 = 5

No. Any real numbers work as long as the triangle is right-angled.

It is the simplest integer triple, making it easy to verify steps.

Yes. Input your numbers and compare with the worked examples.

Review the core formula and calculator phrases for right triangle problems.

Use c = √(a² + b²) when both legs are known.

Use the 3-4-5 triangle pattern for quick right-angle checks.

Try your own values in the calculator.