Physics hw question?

The route followed by a hiker consists of three displacement vectors A,B, and C. Vector A is along a measured trail and is 1550 m in a direction 28.0° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0° east of south. Similarly, the direction of vector C is 39.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A+B+C = 0. Find the magnitudes of vector B and C.

Physics hw question?
This is a very simple problem:





All x-component vectors and y-component vectors need to add up to ZERO.





X: Acos(28°) - Bsin(41°) - Ccos(39°) = 0 [1]





Y: Asin(28°) - Bcos(41°) + Csin(39°) = 0 [2]





A = 1550 m





Now we have 2 equations and 2 unknowns, so we solve for B and C:





Equation [1] becomes





C = [Acos(28°) - Bsin(41°)] / cos(39°)





Substitute C into equation [2]





Asin(28°) - Bcos(41°) + ([Acos(28°) - Bsin(41°)] / cos(39°)) sin(39°) = 0





Asin(28°) + Acos(28°) tan(39°) = Bcos(41°) + Bsin(41°) tan(39°)





A(sin(28°)+cos(28°)tan(39°)) = B(cos(41°)+sin(41°)tan(39°))





Therefore,





B = A(sin(28°)+cos(28°)tan(39°)) / (cos(41°)+sin(41°)tan(39°))





= 1427.65 m





C = 555.81 m