Question

in wexford, the library is 9.4 miles due south of the courthouse and 2.5 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: Identify the right triangle

The library, courthouse, and community swimming pool form a right triangle. The distance from courthouse to library (9.4 miles) and library to pool (2.5 miles) are the legs. Let \( c \) be the distance between courthouse and pool (hypotenuse).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \( a^2 + b^2 = c^2 \), where \( a = 9.4 \), \( b = 2.5 \). So, \( c = \sqrt{9.4^2 + 2.5^2} \).
First, calculate \( 9.4^2 = 88.36 \) and \( 2.5^2 = 6.25 \). Then sum them: \( 88.36 + 6.25 = 94.61 \). Now take the square root: \( c = \sqrt{94.61} \approx 9.7 \).

Answer:

9.7