Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the third side be \(x\). Here \(a = 5\), \(c=12\), then \(x=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(x=\sqrt{12^{2}-5^{2}}=\sqrt{144 - 25}=\sqrt{119}\).

Step3: Calculate the value

\(\sqrt{119}\approx10.9\) (rounded to the nearest tenth).

Answer:

\(10.9\)