Expert: Scott A Wilson - 11/1/2009

Question
I need help with this problem, please:

Two hikers leave a tent at a campground and go separate ways. One hiker walks directly west 15 miles to Ashville, and the other hiker walks directly northeast 9 miles to Bellville. (Assume that the terrain is flat.) How far apart are Ashville and Bellville? Show work. (You may find it helpful to draw a picture, but you do not need to submit it.)

Thank you!

Answer
Put the campground at the origin on an x-y graph.
This would put one town at (-15,0) and the other town up at (9/√2,9/√2).
The 9/√2 is because when (9/√2)² and (9/√2)² are added together as the two legs of a right triangle, the result is getting 40.5 + 40.5, which is 81.  That is 9².

The distance between two points is √((y2-y1)²+(x2-x1)²).
If (x1,y1) = (-15,0) and (x2,y2) = (9/√2,9/√2), then that gives
√((9/√2)²+(9/√2 + 15)²) = √(40.5 +  456.42) = √497.

Now 22² = 484 and 23²=529, so this is in between 22 and 23.