### The **Formula**

The picture below shows the formula for the Pythagorean theorem. In the pictures below, side C is always the hypotenuse. Remember that this formula only applies to right triangles.

**Examples** of the Pythagorean Theorem

When you use the Pythagorean theorem, just remember that the hypotenuse is always 'C' in the formula above . Look at the following examples to see pictures of the formula.

### Conceptual Animation of ** Pythagorean Theorem**

**Video** Tutorial

on How to Use the Pythagorean Theorem

**Step By Step** Examples

of Using the Pythagorean Theorem

##### Example 1 (solving for the hypotenuse)

Use the Pythagorean theorem to determine the length of X

Step 1Identify the legs and the hypotenuse of the right triangle.

The legs have length '6 and '8' . 'X' is the hypotenuse because it is opposite the right angle.See Picture

Substitute values into the formula (remember 'c' is the hypotenuse)

$ A^2+ B^2= \red C^2 \\ 6^2+ 8^2= \red X^2 $

Solve for the unknown

##### Example 2 (solving for a Leg)

Use the Pythagorean theorem to determine the length of X

Step 1Identify the legs and the hypotenuse of the right triangle.

The legs have length '24' and 'X' are the legs. The hypotenuse is 26. See Picture

Substitute values into the formula (remember 'c' is the hypotenuse)

$ \red A^2+ B^2= C^2 \\ \red x^2 + 24^2= {26}^2 $

Solve for the unknown

Remember our steps for how to use this theorem. This problems is like example 1 because we are solving for the hypotenuse.

Step 1Identify the legs and the hypotenuse of the right triangle.

The legs have length '14' and 48 are the legs. The hypotenuse is X. See Picture

Substitute values into the formula (remember 'c' is the hypotenuse)

A^{2} + B^{2} = C^{2}

14^{2} + 48^{2} = x^{2}

Solve for the unknown

Identify the legs and the hypotenuse of the right triangle.

The legs have length '9' and 'X'. The hypotenuse is 10.

Substitute values into the formula (remember 'c' is the hypotenuse)

A^{2} + B^{2} = C^{2}

9^{2} + X^{2} = 10^{2}

Solve for the unknown

Identify the legs and the hypotenuse of the right triangle.

The legs have length '10' and 'X'. The hypotenuse is 20.

Substitute values into the formula (remember 'c' is the hypotenuse)

A^{2} + B^{2} = C^{2}

10^{2} + X^{2} = 20^{2}

Solve for the unknown