The Pythagorean Theorem

If you’ve been doing math for any period of time, you’ve probably run into a formula that looks like this:

a² + b² = c²

This very useful bit of math is called the Pythagorean Theorem, named after Greek mathematician Pythagoras. Put into words, the above equation tells us that the sum of the square of the two legs of a right triangle equals the square of the hypotenuse (the longest side of a right triangle).

This formula has many potential uses. If you know the length of both legs, or one leg and the hypotenuse, of a right triangle, then you can solve for the missing side using the Pythagorean Theorem.

For example, we are given that a = 3 and b = 4. Let’s solve for c.

3² + 4² = c²

9 + 16 = c²

25 = c²

= c

5 = c

You can also use the Pythagorean Theorem to prove whether or not a triangle is a right triangle. For this example, let’s have a = 5, b = 10, and c= 13.

5² + 10² = 13²

25 + 100 = 169

125 = 169

Wait a second! 125 does not equal 169. Therefore, a triangle with sides 5, 10, and 13 is not a right triangle.

Let’s try it again with a triangle with the sides 7, 24, and 25.

7² +24² = 25²

49 + 576 = 625

625 = 625

This triangle is a right triangle!

In a bind where a right triangle is involved? Try out the Pythagorean Theorem and see if it helps!