The diagonal of a right triangle, which contains a 90-degree angle, is called the hypotenuse. This diagonal forms the side of the right triangle directly across from the 90-degree angle. The ancient Greek mathematician Pythagoras developed the formula to calculate the length of the hypotenuse. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides -- that is, a^2 + b^2 = c^2 where “c” is equal to the length of the hypotenuse and “a” and “b” are the lengths of the other two sides.
Draw a right triangle and label the sides a, b and c. “C” should be the hypotenuse and “a” and “b” should be the other two sides.
Label side “a” with the length of 3 and label side “b” with the length of 4.
Calculate the length of the hypotenuse “c” with the formula a^2 + b^2 = c^2. A calculator will be required. The formula should be look like √ (a^2 + b^2) = c. Putting in the numbers from the example yields √(3x3 + 4x4) = c. The answer is the square root of 25, which is 5. Therefore, the length of the diagonal of this right triangle is 5.