# Pythagorean Theorem: Calculate hypotenuse or legs

TOPICS: Calculate Leg     Calculate Hypotenuse     Calculate One Side     Sample Exercises     Worked Examples     Solutions

Of all the Pythagorean Theorem problems we might be given, one of the most common is where we are asked to calculate the hypotenuse of a right triangle knowing the measurements of both legs, or where we must calculate the length of one of the legs knowing the hypotenuse and the other leg.

This type of problem is easy to solve if we know how. Really, the solution to all of them is based on the same formula. We should know that, according to the Pythagorean Theorem:

1. The hypotenuse of a right triangle is equal to the square root of the sum of the squares of the legs.
2. The leg of a right triangle is equal to the square root of the hypotenuse squared minus the other leg squared.

In the following image you can see a visual representation of the formulas that you have to use to solve these Pythagorean Theorem exercises where you are asked to calculate the hypotenuse knowing the two legs or one of the legs knowing the hypotenuse and the other leg.

Now we’re going to look at three worked examples on the Pythagorean Theorem where we are asked to calculate one of the sides of a right triangle, either the hypotenuse or one of the legs. Below we have a picture of each of these exercises so you get an idea of what’s going on, but if you find them interesting, you can download them in PDF form using the two links at the bottom of the text.

First exercise: Calculate the hypotenuse

Second exercise: Calculate a leg

Third exercise: Calculate one of the sides of a right triangle