The Pythagorean Theorem describes the relationship between the side lengths of a right triangle.
What the theorem says
In a right triangle, the sum of the squares of the two leg lengths equals the square of the hypotenuse length.
Legs and hypotenuse
Sides a and b are the legs. Side c is opposite the right angle and is the hypotenuse.
Formula
a^2 + b^2 = c^2
In this formula, c must represent the hypotenuse.
- a
- — length of the first leg
- b
- — length of the second leg
- c
- — length of the hypotenuse
Example
Legs 3 and 4
Substitute the two leg lengths and solve for the hypotenuse.
\begin{aligned}3^2 + 4^2 &= c^2 \\ 9 + 16 &= c^2 \\ 25 &= c^2 \\ c &= 5\end{aligned}
Make sure c is the hypotenuse
The Pythagorean Theorem applies only to right triangles. In the formula, c represents the hypotenuse, not just any side.