Question

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

Explanation:

Step1: Identify the theorem

Since it's a right - triangle, use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, the hypotenuse \(c = 18\) and one leg \(a = 16\), and we want to find the other leg \(b\).

Step2: Rearrange the formula

We can rewrite the Pythagorean theorem as \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute values

Substitute \(c = 18\) and \(a = 16\) into the formula: \(b=\sqrt{18^{2}-16^{2}}=\sqrt{(18 + 16)(18 - 16)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{(34)(2)}=\sqrt{68}\).

Step4: Calculate and round

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

Answer:

8.2