*There is one last type of problem you might run into where you use the Pythagorean theorem to write some type of algebraic expression.This is something that you will not need to do in every course, but it does come up.*

In each example, pay close attention to the information given and what we are trying to find.

This helps you determine the correct values to use in the different parts of the formula. The side opposite the right angle is the side labelled \(x\). When applying the Pythagorean theorem, this squared is equal to the sum of the other two sides squared.

In other situations, you will be trying to find the length of one of the legs of a right triangle.

You can still use the Pythagorean theorem in these types of problems, but you will need to be careful about the order you use the values in the formula. The side opposite the right angle has a length of 12.

Since no figure was given, your first step should be to draw one.

The order of the legs isn’t important, but remember that the hypotenuse is opposite the right angle.

At that moment, what is the shortest distance between the two hikers? Label any unknown value with a variable name, like x.

Due south and due west form a right angle, and the shortest distance between any two points is a straight line.

As in the formula below, we will let a and b be the lengths of the legs and c be the length of the hypotenuse.

Remember though, that you could use any variables to represent these lengths.

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