Question

find the length of the third side. if necessary, write in simplest radical form.

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 8\) (hypotenuse) and \(a=\sqrt{55}\). So \(x^{2}+(\sqrt{55})^{2}=8^{2}\).

Step2: Simplify the equation

\(x^{2}+55 = 64\). Then \(x^{2}=64 - 55\).

Step3: Solve for \(x\)

\(x^{2}=9\), so \(x=\sqrt{9}=3\).

Answer:

\(3\)