[scw287]

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 29.0° 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 14.0° 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.


I am able to set up the problem pretty easily using the component method and I end up with these two equations 1550cos(29)+Bsin(41)-cos(14)=0 & 1550sin(29)-Bcos(41)+Csin(14)=0. I'm not really sure how to solve these two equations. I think that you set both of them equal to 0 but that really didn't help me. Also I'm not sure how you would use trig and the pathogrean theorem when there are three vectors. Please can you help me?

[ebaines]

Your technique seems valid- you ended up with 2 equations in 2 unknown (B and C), so you should be able to solve for B and C. There is a typo in your first formula -you're missing the factor C in front of the cos(14).

Here's another approach: since you know all the bearings involved you can figure out the interior angles of the triangle that the hiker followed (for example, the angle between A and C is 29+14 = 43 degrees), and since you know the length of A, you can use the law of sins to calculate lengths B and C.