**The hypotenuse of a right triangle is calculated by finding the square root of the sum of the squares of the triangle's legs.** It can be expressed using the formula c = √(a^{2} + b^{2}), where a and b represent the legs of the triangle and c indicates the hypotenuse.

A right triangle is a triangle comprising two sides, known as legs, and a hypotenuse, which is identified as the triangle's longest segment. The intersection of the two legs form a 90-degree angle, which sits opposite to the hypotenuse. The formula for finding a right triangle's hypotenuse is derived from the famous Pythagorean Theorem, which is given as a^{2} + b^{2} = c^{2}. This special property of right triangles was discovered and named after the Greek mathematician Pythagoras. The theorem shows the correlation between the triangle's legs and its hypotenuse, where it states that the sum of the squares of the triangle's legs is equal to the sum of the square of the hypotenuse. Some of the practical applications of the Pythagorean Theorem involves various fields in science, architecture and engineering.

A special type of right triangle is the 45-degree and 45-degree right triangle, where the lengths of its legs are equal. To find the hypotenuse, the leg's length is multiplied by the square root of 2.