What is the Pythagorean theorem used for?

The Pythagorean theorem is a fundamental principle in geometry that specifically applies to right triangles, which are triangles that contain one angle measuring 90 degrees. 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 can be mathematically expressed as (a^2 + b^2 = c^2), where (c) is the length of the hypotenuse and (a) and (b) are the lengths of the other two sides.

This property allows us to calculate the length of any one side of a right triangle if the lengths of the other two sides are known. For example, if the lengths of the two sides are known, one can rearrange the formula to find the length of the hypotenuse or one of the legs of the triangle, making the theorem an invaluable tool in many practical applications involving right triangles, including architecture, navigation, physics, and various fields of engineering and design.

The other options relate to different mathematical concepts: calculating the area of a triangle requires a different formula, determining the volume of a cylinder involves the