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 Perimeter of a Triangle
How to Find the Long Side Dimension on a Right Triangle
How to Bisect a Triangle
How to Find Side Lengths of Triangles
How to Find the Area of Squares
How to Calculate Ramp Length
How to Calculate the Diagonal of a Triangle
How to Find the Area of a Rectangle
How to Calculate Triangle Dimensions
How to Calculate Acute Angles
How to Find One Side of an Isosceles Triangle
How to Calculate Sides of a Triangle
How to Find the Perimeter of a Right Triangle
How to Solve a Hexagon
How to Find the Area of Triangles & Trapezoids
How to Find the Surface Area of Triangles
How to Calculate Volume of a Rectangular Prism
How to Convert Square Dimensions to Round
How to Calculate the Square Meters in a Triangle
Characteristics of Aquatic Plants

Dont Go!

We Have More Great Sciencing Articles!