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 hypotenuse and legs

The hypotenuse \(c = 18\) and one leg \(a = 16\). We use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(b\) is the unknown side.

Step2: Rearrange the Pythagorean theorem

We get \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute the values

Substitute \(a = 16\) and \(c = 18\) into the formula: \(b=\sqrt{18^{2}-16^{2}}=\sqrt{(18 + 16)(18 - 16)}=\sqrt{34\times2}=\sqrt{68}\).

Step4: Calculate and round

\(\sqrt{68}\approx 8.2\).

Answer:

8.2