How to Find the Length of the Sides on a Right Angle Triangle

A right triangle has one angle that is equal to 90 degrees. The other two angles are acute (equal to less than 90 degrees). The longest side of a right triangle is called the hypotenuse. The Pythagorean theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides. Using this theorem, you can find one of the sides when the other two are given. Alternatively, you can calculate any two sides if the third one is given together with the smallest of the acute angles.

Things You'll Need

• Calculator

Instructions

Calculate the Third Side if Two Sides Are Known

1. Calculate the square of the hypotenuse. That is, raise the hypotenuse to the second power. For example, if the hypotenuse is 10, 10^2 = 100.

2. Calculate the square of the second known side. For example, if this side is 6, 6^2 = 36.

3. Subtract the square of the second side from the square of the hypotenuse. In this example, 100 - 36 = 64.

4. Take the square root of the difference to calculate the third side of the right triangle. In this example, the third side is the square root of 64, or 8.

Calculate Two Sides if One Side and the Smallest Acute Angle Are Known

1. Calculate the sine of the smallest acute angle. For example, if the smallest acute angle is 30 degrees, the sine would be 0.5.

2. Calculate the cosine of the smallest acute angle. In this example, the smallest acute angle is 30 degrees, so the cosine would be 0.866.

3. Multiply the hypotenuse by the sine value to calculate the side that is opposite the angle. For example, if the hypotenuse is 10, the opposite side would 10 x 0.5 = 5.

4. Multiply the hypotenuse by the cosine value to calculate the side that is adjacent to the angle. In this example, the adjacent side is 0.866 x 10 = 8.66.

References

• Mathworld: RightTriangle