Vector Magnitudes given only direction--help! 1. The problem statement, all variables and given/known data You leave your campsite to go get supplies at a store. You travel 230M at an angle 31 degrees south of east to get there(I'll call this vector A for simplicity's sake). On the way back to camp, you go a distance B at 43 degrees north of west and a distance C at 60 degrees south of west. Find the distances B and C. 2. Relevant equations Not sure. I've tried the law of sins: sin(a)/A=sin(b)/B=sin(c)/C. I can't think of anyway to use the dot product or cross product to solve this problem, though that's what the section is supposedly about. 3. The attempt at a solution I used the law of sins first. Initially, I used the angles provided and got a wrong answer, as I didn't manipulate the measures of the angles. Later, I tried making the X-axis go along A and adjusting the angle between A and B to 12 degrees and the angle between B and C as 103 degrees. This also gave a wrong answer of 213.95. (I had the sin(103)/230=sin(65)/B)). I got the 65 degree based on triangles having 180 degrees. I've also attempted setting up a system of equations for the components of B and C, as I know that the X and Y components of B and C must add up to be the opposite of the X and Y components of vector A, but I hit a wall there as well. I haven't attempted finding the distance of C until I am sure B is correct. I have no idea why the dot or cross product is pertinent in the case, if it is at all. I have a feeling I am either missing a very simple concept, making a math error in the angles I am using, or just making the problem harder than it needs to be. Please point me in the right direction!! Thanks for any help, it's really appreciated.