Question

Your school is 5 miles west and 2 miles south of your apartment. You bicycle 3 miles east and then 5 miles south from your apartment to a friend's house. Find the distance between your friend's house and your school.

Answer 1

Let's draw a diagram of the situation. A will be the apartment, S will be the school and F will be the friend's house:

We have formed a right triangle according to the data given. Since you went 3 miles east, and you'd normally have to go 5 miles west to the school, the length of the horizontal distance is 8 miles.

Since you went 5 miles south, and you'd only go 2 miles south to school, the lenght of the vertical distance will be 3 miles.

Thus, we have a right triangle with sides 8 and 3, and we want to find its hypotenuse. Using the Pythagorean theorem, we get:

`h=\sqrt[]{8^2+3^2}=\sqrt[]{64+9}=\sqrt[]{73}\approx8.54.`

So the school is approximately 8.54 miles from your friend's house.