Final answer:
To find the distance from the library to the park, we subtract the distance from Sami's home to the library (4 miles) from the distance from the library to the football field (18 miles), resulting in 14 miles. To find the distance from the park to the football field, we use the Pythagorean theorem with Sami's home to the football field as the hypotenuse (22 miles) and Sami's home to the park (4 miles) as one leg, revealing that the park is approximately 21.63 miles from the football field.
Step-by-step explanation:
The question involves determining the distances in a right-angled triangle situation, where Sami's home, the park, and the football field create the vertices of the triangle. Since Sami lives directly east of the park and the football field is directly south of the park, we're dealing with a scenario where the distance from Sami's home to the park and the distance from the football field to the park form the two perpendicular sides of a right-angled triangle.
The library sits on the line formed between Sami’s home and the football field, which means it lies on the hypotenuse of the right-angled triangle. The library is 4 miles from Sami’s home (one leg of the triangle), and the football field is 18 miles from the library (the hypotenuse minus one leg).
First, let's find the distance from the library to the park. Since we know the football field is 18 miles from the library, and this distance is along the hypotenuse, we subtract the distance from Sami's home to the library (4 miles) to find the distance from the library to the park:
Distance from library to park = hypotenuse (from library to football field) - one leg (from library to Sami's home) = 18 miles - 4 miles = 14 miles.
Now, let's find the distance from the park to the football field. The full hypotenuse is the distance from Sami's home to the football field, which is the distance from Sami's home to the library (4 miles) plus the distance from the library to the football field (18 miles).
Full hypotenuse (from Sami's home to football field) = 4 miles + 18 miles = 22 miles.
Using the Pythagorean theorem, we can calculate the distance from the park to the football field as the other leg of the right triangle (a² + b² = c², where c is the hypotenuse).
Distance from park to football field (b)² = (c)² - (a)² = 22² - 4² = 484 - 16 = 468.
Therefore, Distance from park to football field (b) = √468 ≈ 21.63 miles.