After school, Ann skateboards directly from school to an ice cream parlor and then from the ice cream parlor to a movie theater. The ice cream parlor is 6 kilometers south of the school and the movie theater is 6 kilometers east of the ice cream parlor. What is the straight-line distance between the school and the movie theater? If necessary, round to the nearest tenth.
kilometers
To find the straight-line distance between the school and the movie theater, we can use the Pythagorean theorem since the path forms a right triangle.
1. The distance from the school to the ice cream parlor is 6 kilometers south.
2. From the ice cream parlor to the movie theater, it’s 6 kilometers east.
Now, you can visualize a right triangle where:
– One leg (south) = 6 kilometers
– The other leg (east) = 6 kilometers
Using the Pythagorean theorem:
[ c = sqrt{a^2 + b^2} ]
Where ( a ) and ( b ) are the legs of the triangle.
Here,
[ a = 6 , text{km} ]
[ b = 6 , text{km} ]
Now, calculate:
[ c = sqrt{(6)^2 + (6)^2} = sqrt{36 + 36} = sqrt{72} approx 8.49 ]
Rounded to the nearest tenth, the straight-line distance is approximately 8.5 kilometers.
So, the answer is 8.5 kilometers.