The Pythagorean 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:
\[ c^2 = a^2 + b^2 \]
where \( c \) represents the length of the hypotenuse, and \( a \) and \( b \) represent the lengths of the other two sides. This theorem is fundamental in geometry and is widely used in various applications, including architecture, physics, and engineering.
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