Question

in arcadia, the library is 12 kilometers due south of the courthouse and 5 kilometers due west of the community swimming pool. what is the distance between the courthouse and the community swimming pool? kilometers

Explanation:

Step1: Identify right - triangle

The positions form a right - triangle. The distance from library to courthouse is one leg ($a = 12$ km), and the distance from library to swimming pool is the other leg ($b = 5$ km). We want to find the hypotenuse $c$ (distance between courthouse and swimming pool).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 12$ and $b = 5$ into the formula: $c=\sqrt{12^{2}+5^{2}}=\sqrt{144 + 25}=\sqrt{169}$.

Step3: Calculate the result

$\sqrt{169}=13$.

Answer:

13