How It Works

The calculator applies the Pythagorean theorem to a right triangle. If the two legs are known, it calculates the hypotenuse. If the hypotenuse and one leg are known, it calculates the remaining leg.

a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse. The hypotenuse can be found with c = √(a² + b²), while a missing leg can be found with a = √(c² − b²).

Example

For example, a right triangle with legs of 3 and 4 has a hypotenuse of 5 because √(3² + 4²) = √25 = 5.

Frequently Asked Questions

What is the Pythagorean theorem?

The Pythagorean theorem states that the square of the hypotenuse equals the sum of the squares of the two legs of a right triangle: a² + b² = c².

How do you find the hypotenuse of a right triangle?

Square both legs, add the results, and take the square root. The formula is c = √(a² + b²).

How do you find a missing leg?

Square the hypotenuse and the known leg, subtract the known leg's square from the hypotenuse's square, and take the square root. The formula is a = √(c² − b²).

What is the hypotenuse of a triangle with sides 3 and 4?

If 3 and 4 are the two legs of a right triangle, the hypotenuse is 5. This is the well-known 3-4-5 right triangle.

Does the Pythagorean theorem work for every triangle?

No. The Pythagorean theorem applies specifically to right triangles, where one angle measures exactly 90 degrees.

Which side is the hypotenuse?

The hypotenuse is the side opposite the 90-degree angle. It is also the longest side of a right triangle.