Question

Item 18 You and your friend are standing back-to-back. Your friend runs 20 feet forward and then 15 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?

Answer 1

You threw the baseball 40 feet.

This can be represented as two right triangles.  The legs of your friend's triangle, the forward distance and distance right, are 15 and 20.  Using the Pythagorean theorem, we find the diagonal distance from your friend's starting point:

20²+15²=c²
400+225=c²
625=c²

Take the square root of both sides:
√625=√(c²)
25=c

The legs of your right triangle are 12, your distance forward, and 9, your distance right:
12²+9²=c²
144+81=c²
225=c²

Take the square root of both sides:
√225=√(c²)
15=c

The total diagonal distance is 25+15=40 feet.

Answer 2

To find this answer it is best to draw it out. Please see the attached picture. You will end up needing to find it 2 hypotenuse. I have shown how to find the hypotenuse using the Pythagorean theorem. You add these together to find the distance the baseball is thrown. The answer is 40 feet.