Answer:
12 miles
Step-by-step explanation:
A right triangle is formed, where the distance between the library and the courthouse is one leg ( = 9 miles), the distance between the library and the swimming pool is the other leg (let's call it x), and the distance between the swimming pool and the courthouse is the hypotenuse ( = 15 miles).
From Pythagorean theorem:
15² = 9² + x²
225 - 81 = x²
x = √144
x = 12 miles
