Pythagorean Theorem

How to Use The Pythagorean Theorem

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.

The Pythagorean Theorem

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.

Examples of the 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

Example 1 Step 1

Identify 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

The hypotenuse is red in the diagram below:
Step 2

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

A2 + B2 = C2
62 + 82 = X2

Step 3

Solve for the unknown

Example 2 (solving for a Leg)

Use the Pythagorean theorem to determine the length of X

Example 2 Step 1

Identify 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

The hypotenuse is red in the diagram below:
Step 2

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

A2 + B2 = C2
x2 + 242 = 262

Step 3

Solve for the unknown

Problem 1

Find the length of X

Pythagorean Theorem Problem

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

Step 1

Identify 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

Step 2

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

A2 + B2 = C2
142 + 482 = x2

Step 3

Solve for the unknown

The hypotenuse is red in the diagram below:
Problem 2

Use the Pythagorean theorem to calculate the value of X. Round your answer to the nearest tenth.

Pythagorean Theorem Problem

Remember our steps for how to use this theorem. This problems is like example 2 because we are solving for one of the legs.

Step 1

Identify the legs and the hypotenuse of the right triangle.

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

Step 2

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

A2 + B2 = C2
92 + X2 = 102

Step 3

Solve for the unknown

Problem 3

Use the Pythagorean theorem to calculate the value of X. Round your answer to the nearest hundredth.

Pythagorean Theorem Problem

Remember our steps for how to use this theorem. This problems is like example 2 because we are solving for one of the legs.

Step 1

Identify the legs and the hypotenuse of the right triangle.

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

Step 2

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

A2 + B2 = C2
102 + X2 = 202

Step 3

Solve for the unknown