Visualize a triangle, where the string represents the hypotenuse and the line between Tom and Kathy represents one of the legs. The Pythagorean theorem states that if one knows the length of two sides of a triangle, the length of the third side can be determined, using the formula \(a^2 + b^2 = c^2\). In this case, \(300^2 + b^2 = 500^2\).
\(90,000 + b^2 = 250,000\)
\(b^2 = 250,000 - 90,000\)
\(b^2 = 160,000\)
\(b = \sqrt{160,000}\)
\(b = 400\)