What is the formula that expresses the relationships among the sides of a right triangle?

The formula that expresses the relationships among the sides of a right triangle is the Pythagorean theorem. 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. Mathematically, this is expressed as ( a^2 + b^2 = c^2), where (c) represents the length of the hypotenuse and (a) and (b) represent the lengths of the other two sides.

Understanding the Pythagorean theorem is foundational in various fields, including plumbing, where it can be applied to ensure correct measurements and alignments when installing fixtures and piping systems. This theorem not only helps in verifying the integrity of a right triangle but also aids in solving problems related to space and angles, which can be encountered in practical plumbing scenarios.

The other concepts, such as trigonometric ratios, while also related to triangles, specifically deal with the relationships between the angles and sides of triangles rather than the direct relationship among the sides of a right triangle. Circle theorem and Euclidean formula do not pertain to the properties of right triangles in the same