According to the Pythagorean theorem, what is the equation used to relate the sides of a right triangle?

The equation that relates the sides of a right triangle, as stated in the Pythagorean theorem, is a² + b² = c². In this context, 'a' and 'b' represent the lengths of the two legs of the right triangle, while 'c' represents the length of the hypotenuse, which is the side opposite the right angle. This theorem is fundamental in geometry and is used to determine the length of one side of a right triangle when the lengths of the other two sides are known.

The Pythagorean theorem is essential in various applications, including construction, navigation, and physics, as it allows for the calculation of distances and angles. Additionally, this equation is derived from the geometric properties of right triangles, providing a mathematical foundation for reasoning about shapes in Euclidean space.

The other statements represent different mathematical concepts but do not pertain to the relationships defined by the Pythagorean theorem. The equation involving sine and cosine relates to trigonometric identities, while the other two equations do not accurately describe the relationships between the sides of a right triangle. Understanding the Pythagorean theorem is crucial for anyone working with right triangles in any practical or theoretical capacity.