what should be the angle between 2 forces of magnitude 1 N and 13 N so that the resultant is 6*(5)^1/2 N. find the angle between the resultant and 1 N force.

I think you should probably use law of cosines.
Law of cosines - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Law_of_cosines)

Right - law of cosines will get you the angle between the 2 known forces. Then you could use the law of sines to find the angle between the resultant and the 1N force.