The route followed by a hiker consists of three displacement vectors A, B and C. Vector A is along a measured trail and is 2500 m in a direction 25.8° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 43.1° east of south. Similarly, the direction of vector C is 32.2° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + B + C = 0. Calculate the magnitude of vector B.
This is for my physics course. The teacher expects us to know vectors already, and I have never had them. I have tried for over 3 hours to solve this question. No luck.
The Attempt at a Solution
I realize that the vectors form a triangle since the displacement is 0. So I tried to assign the correct values to the interior of the triangle, and then use the law of sines to find the magnitude of vector b.
I bet there is a better way to solve this but I have no idea.
Please help me guys!