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Math: Basic Tutorials : Pythagorean Theorem
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.
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.
Summary and Worksheet
- Summary: The Pythagorean Theorem - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: The Pythagorean Theorem - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
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