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 \(a = 2\) and \(b\) (unknown) and hypotenuse \(c=3\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 2\) and \(c = 3\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=3^{2}-2^{2}=9 - 4=5\).

Step3: Solve for \(b\)

Take the square root of both sides. Since \(b>0\) (length of a side), \(b=\sqrt{5}\).

Answer:

\(\sqrt{5}\)