Question

in ashland, the library is 8.5 kilometers due south of the courthouse and 2.5 kilometers due west of the community swimming pool. what is the distance between the courthouse and the community swimming pool? if necessary, round to the nearest tenth. kilometers

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 2.5\) (distance library - pool), \(b=8.5\) (distance library - courthouse). The distance \(d\) between courthouse and pool is \(d=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values

\(d=\sqrt{2.5^{2}+8.5^{2}}=\sqrt{6.25 + 72.25}=\sqrt{78.5}\)

Step3: Calculate the square - root

\(\sqrt{78.5}\approx8.86\approx8.9\)

Answer:

\(8.9\)