AlgebraStructure & Method · Book 1All Chapters

Irrational Numbers

11-6The Pythagorean Theorem

Overview

In a right triangle with legs a, b and hypotenuse c: a² + b² = c².

Key ideas

  • Hypotenuse is opposite the right angle (longest side).
  • Use to find a missing side.
  • Works only for right triangles.

Worked examples

Example 1

Problem. Legs 3 and 4. Hypotenuse?

Solution. 5

Example 2

Problem. Hypotenuse 13, one leg 5. Other leg?

Solution. 12

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Legs 6, 8. Hypotenuse?

  2. 2.

    Legs 5, 12. Hypotenuse?

  3. 3.

    Hypotenuse 17, leg 8. Other leg?

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

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

  2. 2.

    The hypotenuse of a right triangle is 13 and one leg is 5. Find the other leg.