The route followed by a hiker consists of three displacement vectors A, B and C. Vector A is along a measured trail and is 3500 m in a direction 24.4° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 42.7° east of south. Similarly, the direction of vector C is 36.5° 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.
A + B + C = 0
a^2 + b^2 = c^2
a/sinA = b/sinB = c/sinC
The Attempt at a Solution
I worked this one out completely to what I believed to be the answer. I first set the vectors up in head to tail fashion so they created a triangle, I then used the law of sines to determine angle B which I know is definitely right, so I'm thinking is that where my error lies is the angles of A and C. When I went over this recitation for some reason I had that C = 60.5 deg, but that's only part of the angle right? Shouldn't that be added to 24.4? But if I add those together A sums up to be about 10.8 which makes no sense at all so I'm definitely doing something wrong.