Calculating Net Displacement Vector for Sparky's Run Using Law of Cosines

[mugzieee]

Jim's dog Sparky runs 50.0m northeast to a tree, then 70.0m west to a second tree, and finally 20.0m south to a third tree.Calculate Sparky's net displacement vector.
I drew a picture and got an unknown triangle, which yileds the use of law of cos. I applies law of cos, to find an angle, and i get an angle to be 180 degrees. I know this value is wrong, but i know I will need at least one measure of an angle to compute the problem. I just don't see why the law of cos would go wrong here, can anybody help me out.

 

[theCandyman]

The dog does not run in a triangle, if he did, net displacement would be zero. Try redrawing the picture. I have the exact same physics text, keep in mind northeast implies exactly 45 degrees.

 

[HallsofIvy]

Looks to me like the simplest way to do this problem is to reduce the first "run" to components. running 70 yards NE, Sparky runs 70(√(2)/2)= 35√(2) or about 49.5 feet east and 49.5 feet north. Now subtract the distances west and south from those to get the dogs final position. You can calculate distance and angle from his original position from that.

 

[Gamma]

or draw your diagram to scale. For example say 1 inch = 10 m.