The park is 6 mi due east of Freeport High School, and the library is 4 mi due west of the school. The police department is located due north of the school and is 5 mi from the library.
How far is the police department from the park? Round to the nearest tenth of a mile.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²): c² = a² + b²
First, we need to express symbols: b - side of the right triangle (distance between police department and Freeport High School). a1 - side of the first right triangle (distance between library and Freeport High School). a2 - side of the second right triangle (distance between park and Freeport High School). c1 - hypotenuse of the first triangle (distance between police department and library). c2 - hypotenuse of the second triangle (distance between police department and park).
Therefore, we need to calculate c2. It is given: a2 = 6 mi a1 = 4 mi c1 = 5 mi
First, let's calculate b, which is a common side for two triangles: c1² = a1² + b² b² = c1² - a1² b² = 5² - 4² b² = 25 - 16 b² = 9 √b² = √9 b = 3.
We know b, now we can calculate c2: c2² = a2² + b² c2² = 6² + 3² c2² = 36 + 9 c2² = 45 √c2² = √45 c2 = 6.7
The distance between police department and park is 6.7 miles.
