Question

channah is designing a court for a new sport that is played on a triangle - shaped court. the longest side of the court measures 23 feet, while the second side measures 11 feet. if the third side of the court makes a right angle with the second side, how long is it, in feet? round your answer to two decimal places. show your work here hint: to add the square root symbol (√□), type
oot\

Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). According to Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 23\) (hypotenuse), \(a=11\), and \(b = x\). So \(x^{2}+11^{2}=23^{2}\).

Step2: Solve for \(x^{2}\)

\(x^{2}=23^{2}-11^{2}\). Calculate \(23^{2}=529\) and \(11^{2}=121\). Then \(x^{2}=529 - 121=408\).

Step3: Solve for \(x\)

\(x=\sqrt{408}\approx20.20\)

Answer:

\(20.20\)