The Pythagorean Theorem Examples Page 1

A right triangle has one leg of length 5 and a hypotenuse of length 16. What is the length of the other leg of the triangle?

Draw a picture to help us visualize:

We need to find a, the length of the remaining leg. Time's a-wastin', so shake a leg.

The Pythagorean Theorem tells us that a² + (5)² = 16², or a² + 25 = 256.

Then a² = 231, so .

Since a is a length, the final answer is .

Another type of problem you may run into is one in which we are told the length of only one side, but we are given additional useful information about a triangle. Emphasis on "useful." Being told what its party affiliation is or the name of its favorite author won't get us anywhere, although it may convince us not to engage it in any political debate or consider any of its book recommendations.