Question

in livingston, the library is due south of the courthouse and due west of the community swimming pool. if the distance between the library and the courthouse is 3.2 kilometers and the distance between the courthouse and the city pool is 6.4 kilometers, how far is the library from the community pool? if necessary, round to the nearest tenth. kilometers

Explanation:

Step1: Identify the right - triangle

The library, courthouse, and community pool form a right - triangle. Let the distance between the library and the courthouse be \(a = 3.2\) km, the distance between the courthouse and the pool be \(c=6.4\) km, and the distance between the library and the pool be \(b\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). We need to find \(b\), so we can rewrite the formula as \(b=\sqrt{c^{2}-a^{2}}\).
Substitute \(a = 3.2\) and \(c = 6.4\) into the formula:

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Step3: Calculate the value

\(\sqrt{30.72}\approx5.5\)

Answer:

\(5.5\)