Question

find the length of the third side. if necessary, write in simplest radical form.
√55
3

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Let \(a = \sqrt{55}\), \(b = 3\). Then \(c^{2}=(\sqrt{55})^{2}+3^{2}\).

Step2: Calculate \(c^{2}\)

\(c^{2}=55 + 9\). Since \((\sqrt{55})^{2}=55\) and \(3^{2}=9\), so \(c^{2}=64\).

Step3: Find \(c\)

Take the square root of both sides: \(c=\sqrt{64}\).

Answer:

\(8\)