Pythagorean triples are useful for applications because they are whole numbers that make the Pythagorean Theorem true. If you are looking for the length of a side of a right triangle, and you know the lengths of two sides, check first to see if you have a right triangle whose sides are a Pythagorean triple. If you do, then you can use that as a shortcut to solve the problem!

### Solving Problems from a Pictorial Representation

**Problem 1:**

Two poles, one that is 6 meters tall, and one that is 11 meters tall, stand on flat ground. A contractor measures the distance between them along the ground, and discovers that the two poles are 12 meters apart at the ground. If the top of each pole must be connected with one wire, how long will that wire be?

Proceed to the next page to start solving this problem.