Question

in vindale, the library is 4 miles due south of the courthouse and 4 miles 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. miles

Explanation:

Step1: Recognize the right - triangle

The library, courthouse, and community swimming pool form a right - triangle. Let the distance between the courthouse and the library be \(a = 4\) miles, the distance between the library and the community swimming pool be \(b = 4\) miles, and the distance between the courthouse and the community swimming pool be \(c\). By the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\).

Step2: Substitute values into the formula

Substitute \(a = 4\) and \(b = 4\) into \(c^{2}=a^{2}+b^{2}\). Then \(c^{2}=4^{2}+4^{2}=16 + 16=32\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{32}\). Simplify \(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\approx4\times1.414 = 5.656\approx5.7\)

Answer:

\(5.7\)