# How to setup vector story problems

I'm studying for my trig final and I know how to do all the math, but I don't always understand how to setup the story problems. Mostly I'm struggling with vector story problems. For example:

Forces of 4lbs and 12lbs act at an angle of 63 deg to each other. Find the magnitude of the resultant force.

Below is the picture I setup of how I think it should work, but I'm really not clear on what needs to be done after this. I think I need to add the two vectors together but I'm not certain. I got b using law of cosines, though I don't even know if that's relevant to this problem. Or, an equivalent way to do it is to put the two vectors tails on top of each other, and then draw the diagonal of the parallelogram formed that has the common vertex as an endpoint. (The $b$ segment you have in your diagram is the other diagonal, not the one you need.)
You can solve this by Law of Cosines but the angle you want is the complement of $63$ degrees, or $117$ degrees. You should see this if you draw it out, especially the first way above.