Question

toby 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 13 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 ($\sqrt{\square}$), type
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Explanation:

Step1: Apply the Pythagorean theorem

Let the third side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 23\), \(a=13\), and \(b=x\). So \(x^{2}+13^{2}=23^{2}\).

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

\(x^{2}=23^{2}-13^{2}\). Calculate \(23^{2}=529\) and \(13^{2}=169\). Then \(x^{2}=529 - 169=360\).

Step3: Solve for \(x\)

\(x=\sqrt{360}\approx18.97\) (rounded to two decimal places).

Answer:

\(18.97\)