Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 1\), \(b\) (unknown) and hypotenuse \(c = 3\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Rearranging for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 1\) and \(c = 3\) into the formula: \(b=\sqrt{3^{2}-1^{2}}=\sqrt{9 - 1}=\sqrt{8}\).

Step3: Simplify

\(\sqrt{8}=2\sqrt{2}\approx2\times1.414 = 2.828\approx2.8\)

Answer:

\(2.8\)