Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the right - triangle formula

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side of a right - triangle) and \(a\) and \(b\) are the other two sides. In this case, if the two given sides are \(a = 5\) and \(b=9\), and we want to find the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 5\) and \(b = 9\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). So \(c=\sqrt{5^{2}+9^{2}}=\sqrt{25 + 81}=\sqrt{106}\).

Step3: Calculate the value

\(\sqrt{106}\approx10.3\)

Answer:

\(10.3\)