In the Pythagorean theorem, what does the letter 'c' represent?

In the Pythagorean theorem, the letter 'c' specifically represents the hypotenuse of a right triangle. The theorem itself, expressed as ( a^2 + b^2 = c^2 ), establishes a relationship between the lengths of the two legs (denoted as 'a' and 'b') and the hypotenuse ('c').

The hypotenuse is the side opposite the right angle and is always the longest side in a right triangle. This means that when you apply the theorem, the values of 'a' and 'b' are the lengths of the two legs that form the right angle, while 'c' is the side that connects these two legs and is used to calculate the distance or length based on the two legs.

Understanding this helps clarify the geometric relationships in right triangles and is fundamental for various applications in mathematics and physics, making the identification of 'c' as the hypotenuse crucial for anyone studying geometry.