Let's agree again to the standard convention for labeling the parts of a right triangle. Let the right angle be labeled C and the hypotenuse c. Let A and B denote the other two angles, and a and b the sides opposite them, respectively. The Pythagorean theorem is about right triangles, that is, triangles, one of whose angles is a 90° angle. A right triangle is displayed in the diagram to the right. The right angle be labeled C and the hypotenuse c, while A and B denote the other two angles, and a and b the sides opposite them, respectively, often called the legs of a right triangle.
The Pythagorean theorem states that the square of the hypotenuse is the sum of the squares of the other two sides, that is,
c2 = a2 + b2
This theorem is useful to determine one of the three sides of a right triangle if you know the other two. For instance, if two legs are a = 5, and b = 12, then you can determine the hypotenuse c by squaring the lengths of the two legs (25 and 144), adding the two squares together (169), then taking the square root to get the value of c, namely, 13.
Likewise, if you know the hypotenuse and one leg, then you can determine the other. For instance, if the hypotenuse is c = 41, and one leg is a = 9, then you can determine the other leg b as follows. Square the hypotenuse and the first leg (1681 and 81), subtract the square of the first leg from the square of the hypotenuse (1600), then take the square root to get the value of the other leg b, namely 40.