Enter the lengths m, n, and c of a right angle triangle into the calculator to determine the legs a and b.

Leg Rule Formula

The following formulas are used to calculate the legs a and b, given the hypotenuse (c) and distances n and m in the diagram below. 

a = sqrt (m*c)
b = sqrt (n*c)

What is the leg rule?

Definition:

The leg rule is a rule or set of formulas used in the geometry of a triangle that relates the lengths of two of the sides of the right angle to the projected lengths below them, such as shown in the diagram above.

How to calculate legs of a triangle?

Example Problem:

The following example outlines the steps and information needed to calculate the lengths of the legs of a right-angle triangle.

First, determine the length of the hypotenuse. For this example, the hypotenuse has a total length of 8.

Next, determine the length m in the diagram above. This is the project portion of leg a. In this case, the value is 5.

Next, determine the length of n in the diagram above. This is the project portion of leg b. In this case, the length would be 3.

Finally, calculate the legs a and b using the formula above:

a = sqrt (8*5)

b = sqrt (8*3)

a = 6.322

b = 4.898