Virtual Help icon Virtual Help

  • Chat with library staff now
  • Contact your library
Skip to Main Content

Pythagorean Theorem

The Pythagorean theorem is a special property of right triangles that shows us how the three side lengths are related. It is named after the Greek philosopher and mathematician Pythagoras who lived around 500 BCE. In this module, we will review how to use this theorem to solve for an unknown hypotenuse or leg length in a right triangle. We will also look at some practical applications of the Pythagorean theorem.

Finding the Side Other Than Hypotenuse

Finding the Side Other Than Hypotenuse Transcript

Pythagorean Theorem Application

Pythagorean Theorem Application Transcript

Examples & Activity

Examples

Click on the titles below to view each example.

Example 1. Find the length of the missing side, c.

Image: Right triangle with leg lengths of 15 and 8, and the hypotenuse labelled as c.

Line 1. Identify what we are being asked to find. We are being asked to find the length of the hypotenuse of a right triangle.

Line 2. Write the appropriate formula. This is a right triangle, so we can use the Pythagorean theorem to solve for the length of the hypotenuse. A squared plus b squared equals c squared.

Line 3. Substitute in the given values. 15 squared plus 8 squared equals c squared.

Line 4. Solve the equation. 225 plus 64 equals c squared.

Line 5: 289 equals c squared.

Line 6: square root of 289 equals square root of c squared.

Line 7: c equals 17.

Line 8: Answer the question. The length of the hypotenuse is 17.

Example 2. Find the length of the missing side, b.

Image: Right triangle with one leg lengths of 9 and b, a hypotenuse length of 15.

Line 1. Identify what we are being asked to find. We being asked to find the length of the leg of a right triangle.

Line 2. Write the appropriate formula. This is a right triangle, so we can use the Pythagorean theorem to solve for the length of the leg. A squared plus b squared equals c squared.

Line 3. Substitute in the given values. 9 squared plus b squared equals 15 squared.

Line 4. Solve the equation. 81 plus b squared equals 225.

Line 5: b squared equals 225 minus 81.

Line 6: b squared equals square 144.

Line 6: square root of b squared equals square root of 144.

Line 7: b equals 12.

Line 8: Answer the question. The length of the missing leg is 17.

Activity

Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet

Attribution

Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window