Question

After school, Terrell skateboards directly from school to a skate park and then from the skate park to a movie theater. The skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park. What is the straight-line distance between the school and the movie theater?

Answer 1

To find the straight-line distance between the school and the movie theater, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's call the straight-line distance between the school and the movie theater d. Then, we can represent the trip as a right triangle with sides 8 miles (the southward distance to the skate park) and d (the eastward distance from the skate park to the movie theater). The third side, connecting the school and the movie theater, has a length of 6 miles (the distance between the skate park and the movie theater).

Using the Pythagorean theorem, we can write the equation:

d^2 + 8^2 = 6^2

Expanding and solving for d, we get:

d^2 + 64 = 36
d^2 = 36 - 64
d^2 = -28
d = sqrt(-28)

Since the square root of a negative number is not a real number, this solution is not possible. This means that the path from the school to the movie theater cannot be a straight line. Terrell would have to take a curved path or a path with multiple turns to reach the movie theater

Answer 2

10 Miles

We can use the Pythagorean theorem to find the straight-line distance between the school and the movie theater. Let's call the straight-line distance "d".

d^2 = 8^2 + 6^2 = 64 + 36 = 100

d = sqrt(100) = 10

So the straight-line distance between the school and the movie theater is 10 miles.