Which method is commonly used to find the hypotenuse in a triangle?

The Pythagorean theorem is the most commonly used method for finding the hypotenuse of a right-angled triangle. This 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 is expressed mathematically as ( c^2 = a^2 + b^2 ), where ( c ) represents the hypotenuse, and ( a ) and ( b ) are the other two sides.

To apply the theorem, you simply need to know the lengths of the two shorter sides. By squaring these lengths, adding them together, and then taking the square root of the sum, you can find the length of the hypotenuse. This method is straightforward and provides a clear mathematical procedure, which is essential in both theoretical and practical applications, such as construction and navigation.

The other options do not address finding the hypotenuse directly. Algebraic equations can be used in a variety of contexts but are not specifically tied to the dimensions of a triangle. Calculating area is related to the surface measure of a shape but does not involve the direct relationship between the