Question

in burlington, 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 2 kilometers and the distance between the courthouse and the city pool is 9 kilometers, how far is the library from the community pool? if necessary, round to the nearest tenth. kilometers save answer

Explanation:

Step1: Identify right - triangle

The positions of the library, courthouse, and community swimming pool form a right - triangle. The distance between the library and the courthouse ($a = 2$ km) and the distance between the courthouse and the community pool ($b = 9$ km) are the two legs of the right - triangle. We want to find the hypotenuse $c$ (distance between the library and the community pool).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 2$ and $b = 9$ into the formula: $c=\sqrt{2^{2}+9^{2}}=\sqrt{4 + 81}=\sqrt{85}$.

Step3: Calculate and round

$\sqrt{85}\approx9.2$ (rounded to the nearest tenth).

Answer:

$9.2$