Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 3\), \(b = 5\) and hypotenuse \(c\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Here, we want to find the hypotenuse. Substitute \(a = 3\) and \(b = 5\) into the formula: \(c=\sqrt{3^{2}+5^{2}}\).

Step2: Calculate the squares

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

Step3: Add the numbers inside the square root

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

Answer:

\(\sqrt{34}\)