Question

in stafford, 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 miles and the distance between the courthouse and the city pool is 9 miles, how far is the library from the community pool? if necessary, round to the nearest tenth.

square miles

Explanation:

Step1: Identify right triangle sides

The positions form a right triangle: courthouse (C), library (L), community pool (P). CL=2 miles (leg), CP=9 miles (hypotenuse), LP=? (other leg).

Step2: Apply Pythagorean theorem

$$LP = \sqrt{CP^2 - CL^2} = \sqrt{9^2 - 2^2}$$

Step3: Calculate value

$$\sqrt{81 - 4} = \sqrt{77} \approx 8.8$$

Answer:

8.8