How to Find the Missing Side of a Right Triangle

The Pythagorean theorem works with any right triangle.
••• Wooden Triangle image by Towards Ithaca from Fotolia.com

Right triangles have a consistent ratio between the squares of the two legs and the hypotenuse, known as the Pythagorean theorem. How you find the missing side depends on whether you are looking for the hypotenuse or a leg. The "legs" are the two sides that form the 90-degree right angle. The "hypotenuse" is the other side.

Missing Hypotenuse

    Square the lengths of the two legs if you are looking for the hypotenuse. For example, if the two legs of your right triangle measure 6 inches and 8 inches, square 6 and 8 to get 36 and 64.

    Add the two results from step 1. In this example, the sum of 36 and 64 is 100.

    The square root of the result from step 2 equals the length of the hypotenuse. In this example, the hypotenuse is the square root of 100, or 10.

Missing Leg

    Square the lengths of the known leg and the hypotenuse. For example, if the known leg of your right triangle measures 6 inches and the hypotenuse measures 13 inches, square 6 and 13 to get 36 and 169.

    Subtract the square of the leg from the square of the hypotenuse. In this example, subtract 36 from 169 to get 133.

    The square root of the result from step 2 equals the length of the missing leg. In this example, the missing leg is the square root of 133, or 11.53.

Related Articles

How to Find the Long Side Dimension on a Right Triangle
How to Calculate Sides of a Triangle
How to Find the Missing Slope of a Trapezoid
How to Find the Area of Triangles & Trapezoids
Characteristics of Aquatic Plants
How to Find the Area of a Rectangle
How to Use a Protractor to Measure a Triangle
How to Find the Area of Squares
How to Calculate the Diagonal of a Triangle
How to Find the Area of a Parallelogram
How to Find the Perimeter of a Right Triangle
Test Your Knowledge on Middle School Science
How to Figure Out Square Feet
How to Find the Long Side Dimension on a Right Triangle
How to Calculate Acute Angles
How to Calculate Arctan
How to Calculate Diagonal Distance Between Corners...
How to Calculate a Sigma Value
How to Find One Side of an Isosceles Triangle
What Are the Two Major Components of an Atom?

Dont Go!

We Have More Great Sciencing Articles!