How do you use the Pythagorean theorem?

The Pythagorean states that a2 + b2 = c2 for a right triangle, where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse (the diagonal side).

Say you are given a triangle with legs of lengths 3 and 4, and need to find the length of the hypotenuse. You can write the equation

32 + 42 = c2, where c is the length of the hypotenuse.

This gives

25 = c2, and taking the square root of both sides of the equation gives

5 = c, so the length of the hypotenuses in this case is 5.

Another example:

Say you have a right triangle where the length of one leg is 12 and the length of the hypotenuse is 13, and you need to find the length of the other leg. You can write the equation

a2 + 122 = 132, where a is the length of the unknown leg.

Solving:

a2 + 144 = 169

a2 = 25

a = 5, so in this case, the length of the unknown leg is 5.