Recall the Pythagorean Theorem, or the special relationship between the lengths of the sides of a right triangle using the following formula:

*a ^{2} + b^{2} = c^{2}*

*Source: José de Ribera, Pitágoras, Wikimedia Commons*

Because so much of our world is based on rectangles and right triangles, the Pythagorean Theorem is a very special and important relationship in geometry. There are many relevant applications that require the use of the Pythagorean Theorem.

Engineers and astronomers use the Pythagorean Theorem to calculate the paths of spacecraft, including rockets and satellites.

Architects use the Pythagorean Theorem to calculate the heights of buildings and the lengths of walls.

Athletes even use the Pythagorean Theorem when they are calculating distances, which are important in determining how fast they can run or where a ball needs to be thrown.

In this lesson, you will practice using the Pythagorean Theorem to solve a variety of application problems. In doing so, you will work with irrational numbers and may need to approximate the value of an irrational number.