What is the primary use of the Pythagorean theorem?

The Pythagorean theorem is primarily used to find the length of a side in a right triangle. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed mathematically as ( a^2 + b^2 = c^2 ), where ( c ) represents the hypotenuse and ( a ) and ( b ) are the other two sides.

By employing this theorem, one can easily calculate the length of any unknown side if the lengths of the other two sides are known. This application is fundamental in trigonometry and serves as a critical tool in various fields such as physics, engineering, and architecture where right triangles are often analyzed.

Other options, while related to mathematics, do not pertain to the primary use of the Pythagorean theorem. For instance, finding the area of a triangle uses a different formula (base times height divided by two) and does not require the Pythagorean theorem. The calculation of the volume of a cylinder involves using the formula for the volume based on the area of its base (