Question

find the length of the third side. if necessary, round to the nearest tenth. answer attempt 1 out of 2

Explanation:

Step1: Identify the formula

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(c = 25\) and \(a = 22\), and we want to find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 25\) and \(a = 22\) into the formula: \(b=\sqrt{25^{2}-22^{2}}=\sqrt{(25 + 22)(25 - 22)}=\sqrt{47\times3}=\sqrt{141}\).

Step3: Calculate and round

\(\sqrt{141}\approx11.9\approx11.6\) (rounded to the nearest tenth).

Answer:

11.6