Tom is flying a kite at the end of a 500-foot string. His friend Kathy is standing directly under the kite 300 feet away from Tom. How high is the kite flying?

Tom is flying a kite at the end of a 500-foot string. His friend Kathy is standing directly under the kite 300 feet away from Tom. How high is the kite flying?

Detailed Explanation

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, \(300^2 + b^2 = 500^2\).

\(90,000 + b^2 = 250,000\)

\(b^2 = 250,000 - 90,000\)

\(b^2 = 160,000\)

\(b = \sqrt{160,000}\)

\(b = 400\)

\(90,000 + b^2 = 250,000\)

\(b^2 = 250,000 - 90,000\)

\(b^2 = 160,000\)

\(b = \sqrt{160,000}\)

\(b = 400\)