How to Find the Long Side Dimension on a Right Triangle

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A right triangle is a triangle that has one angle equal to 90 degrees. This is often referred to as a right angle. The standard formula for computing the length of the long side of a right triangle has been in use since the days of the ancient Greeks. This formula is based on the simple mathematical concept known as the Pythagorean Theorem. It's named after Pythagoras, the Greek mathematician who first discovered it.

One side of a right triangle is always longer than the other two sides. This long side is known as the hypotenuse and will always be opposite the right angle of the triangle. The other two sides of the triangle are referred to as the legs.

    Calculate the square of each leg (that is, multiply the length of each leg by itself).

    Add these two values together.

    Take the square root of the result of the addition. This is the length of the hypotenuse.


    • If the legs of the triangle are labeled a and b, and the hypotenuse is labeled c, then the Pythagorean Theorem can be described by this equation, where * represents multiplication: (a * a) + (b * b) = (c * c). In text, this equation can be stated as this formula: “the sum of the squares of the legs of a right triangle are equal to the square of the hypotenuse.”

      As an example, consider a right triangle with legs of length 3 and 4. Then (3 * 3) + (4 * 4) = 9 + 16 = 25. The square root of 25 is 5 (that is, 5 * 5 = 25). Therefore, the length of the hypotenuse is 5.

      Calculating the square root of the sum may not be obvious. In this case, a calculator should be used to find the value of the square root. Alternatively, the answer can be expressed using the mathematical symbol for square root (i.e., ?25).


About the Author

Catie Watson has a degree in Computer Science and spent 30 years working as a software engineer for Disney, Unisys and Siemens. She writes about science and technology online and in print publications and was a contributor to the textbook series “Computers, Internet and Society.”

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