Question

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

Explanation:

Step1: Apply the Pythagorean theorem

Let the unknown side be \(a\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 16\) and \(b=12\), so \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute the values

\(a^{2}=16^{2}-12^{2}\)
\(a^{2}=256 - 144\)
\(a^{2}=112\)

Step3: Solve for \(a\)

\(a=\sqrt{112}\)
\(a = 4\sqrt{7}\approx10.6\)

Answer:

\(10.6\)