Pythagorean Theorem Solver

How to calculate the missing side?

For any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

a² + b² = c²

Using the Pythagorean Theorem: an example

Suppose you have a right triangle with side lengths a = 3 and b = 4, and you need to find the hypotenuse c.

Step-by-step calculation:

1. Square the known sides: 3² = 9 and 4² = 16.
2. Add the results together: 9 + 16 = 25.
3. Take the square root of the sum to find the missing side: √25 = 5. Therefore, c = 5.

Frequently Asked Questions

Does this work for all triangles?

No, the Pythagorean Theorem is a fundamental principle specifically for right-angled triangles. It does not apply to acute or obtuse triangles.

What is the hypotenuse?

The hypotenuse is the longest side of a right triangle, always located directly opposite the 90-degree angle.

Can sides be negative?

No, geometric side lengths represent physical distance and must always be positive values.