Right Triangle Calculator

About Right Triangle Calculator

A right triangle has one 90° angle. The Pythagorean theorem relates the sides: a² + b² = c² where c is the hypotenuse.

How to use this calculator

1. Enter the known side lengths of the right triangle, if you have them.
2. Use the hypotenuse as the longest side, labeled c.
3. If one side is missing, the calculator can help determine it from the other two sides.
4. Review the result to see the missing side length and the right triangle relationship.

The formula explained

The formula \(a^2 + b^2 = c^2\) computes the relationship between the two legs, \(a\) and \(b\), and the hypotenuse, \(c\). If one side is missing, you can rearrange the formula to solve for it.

• a = one leg of the right triangle
• b = the other leg of the right triangle
• c = the hypotenuse, the side opposite the 90 degree angle

Step by step method

1. Write the Pythagorean theorem, \(a^2 + b^2 = c^2\).
2. Substitute the two known side lengths into the equation.
3. If the hypotenuse is missing, add the squares of the legs and take the square root. If a leg is missing, subtract the smaller square from the larger square and then take the square root.

Worked example

Problem. A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse.

1. Use the formula: \(a^2 + b^2 = c^2\).
2. Substitute the values: \(6^2 + 8^2 = c^2\), so \(36 + 64 = c^2\).
3. Combine and solve: \(100 = c^2\), so \(c = 10\).

Tips and common mistakes

• Make sure \(c\) is always the longest side, because it is the hypotenuse.
• Do not add the side lengths directly, square them first, then add or subtract.

Frequently asked questions