The Pythagorean Theorem is used to find a missing side length of a right triangle. It only works for right triangles (one with a right angle).

The formula to use is a

The formula to use is a

^{2}+ b^{2}= c^{2}. A really good explanation of the formula and its derivation can be found here.In order to use the theorem, you must know the parts of the triangle. Parts a and b of the theorem are the legs of the triangle. These are the side lengths that make up the right angle. The third side (longest side) is noted as c in the theorem.

Now substitute the values given into the theorem (formula) and solve the equation.

Example: A triangle has a side length of 6 cm and a side length of 8 cm. What is the length of the hypotenuse?

Now substitute the values given into the theorem (formula) and solve the equation.

Example: A triangle has a side length of 6 cm and a side length of 8 cm. What is the length of the hypotenuse?

6

36 + 64 = c

100 = c

√100 = √c

10 = c

^{2}+ 8^{2}= c^{2}36 + 64 = c

^{2}100 = c

^{2}√100 = √c

^{2}10 = c

Example: A triangle has a side length of 6 cm and a hypotenuse length of 12 cm. What is the length of the missing side?

a

a

a

a

√a

a = √108

a = 6√3

Picture of triangle above from http://en.wikibooks.org/wiki/File:Right_triangle_shows_hyp_legs.PNG

a

^{2}+ 6^{2}= 12^{2}a

^{2}+ 36 = 144a

^{2}+ 36 – 36 = 144 – 36a

^{2}= 108√a

^{2}= √108a = √108

a = 6√3

Picture of triangle above from http://en.wikibooks.org/wiki/File:Right_triangle_shows_hyp_legs.PNG