Pythagorean Theorem

A right triangle has one angle that is 90° (i.e., a right angle). The side opposite the right angle is called the hypotenuse, often labeled c, while the other two sides of the triangle (legs) are often labeled a and b.

For a right triangle with legs a and b and hypotenuse c: a² + b² = c²

• Which leg is a or b is irrelevant in the use of the Pythagorean Theorem.
• The Pythagorean Theorem only works for right triangles.

Putting the formula into words, the square of the length of one leg plus the square of the length of the other leg equals the square of the long-side opposite the right angle.

Applying the Pythagorean Theorem

Given any two sides of a right triangle, it is possible to calculate what the length of the third side must be. For example:

Pythagorean Theorem: a² + b² = c²

a = 3, b = 4, c = ?

3² + 4² = c²

9 + 16 = c²

25 = c²

c = 5