How to Find the Length of One Side of a Right-Angled Triangle

A right triangle always has a 90 degree angle.

A right-angled triangle, or simply a right triangle, gets its name from its 90 degree angle. The 90 degree angle causes the other two angles to add up to 90 degrees, totaling 180 degrees in the triangle. This is true for every right triangle. Because these angles do not vary, a standard formula can be used to find the length of any side or "leg" of the right triangle, given you have the length of the other two sides. This formula is the Pythagorean Theorem -- A^2 + B^2 = C^2. "C" is always equal to the longest leg or the hypotenuse. "A" and "B" are the remaining two legs -- either one can be the base.

Things You'll Need

• Calculator

Instructions

Finding the Hypotenuse

1. Identify the lengths given for A and B.

2. Square the length of A, then square the length of B.

3. Calculate the length of A^2 added to the length of B^2. That number is equal to C^2. Find the square root to find the length of C.

Finding the Legs

1. Identify the lengths of the two given sides, C and either A or B. This example is for finding A for the purpose of clarity, but these steps can also be used to find B.

2. Square the length of C, then square the length of B.

3. Subtract B^2 from C^2. That number is equal to A^2. Find the square root to find the length of A.

Tips & Warnings

• To "square" a value, multiple it by itself. For example, 3^2, or 3 squared, is the same as saying 3 times 3, which equals 9. So, 3^2 equals 9.

• "C" will always be the longest leg. If your calculations find otherwise, you have made a mistake.

References

• Wolfram Mathworld: Right Triangle