Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 3\), \(b = 5\), and we need to find the hypotenuse \(c\).
$$c=\sqrt{3^{2}+5^{2}}$$

Step2: Calculate the squares

Calculate \(3^{2}=9\) and \(5^{2}=25\).
$$c=\sqrt{9 + 25}$$

Step3: Add the values

\(9+25 = 34\).
$$c=\sqrt{34}$$

Answer:

\(\sqrt{34}\)