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.

blank mi

The answer is 6.7 mi.

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):

c ² = 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:

c1 ² = a1² + b²

b² = c1 ² - a1²

b² = 5 ² - 4²

b² = 25 - 16

b² = 9

√b² = √9

b = 3.

We know b, now we can calculate c2:

c2 ² = a2² + b²

c2 ² = 6² + 3²

c2 ² = 36 + 9

c2 ² = 45

√c2 ² = √45

c2 = 6.7

The distance between police department and park is 6.7 miles.