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 \(a = 5\), \(b\) is the unknown side, and \(c = 12\). Let the unknown side be \(x\). Then \(5^{2}+x^{2}=12^{2}\).

Step2: Rearrange the formula

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

Step3: Solve for \(x\)

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

Answer:

\(10.9\)