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## Homework Statement

There are two forces. One has a magnitude of 8 N and acts at an angle of 30 degrees on the resultant vector. The resultant vector is 15 N.

## Homework Equations

equations for components (|a|cosx for horizontal and |a|sinx for vertical)

cos law and sin law

basic trig

## The Attempt at a Solution

First, I drew a diagram. Because the direction of the resultant is not stated, I positioned it going south. I then drew the known vector 30 degrees from the tail of the resultant. So it's tip acted 30 degrees on the tail of the resultant, as stated in the problem. I labelled that as b. Then I drew in the unknown vector, which I labelled as a. It makes an unknown angle with the resultant and has an unknown magnitude.

I tried using the cos law/sin law way of solving this, but all I could figure out is that vector a makes an angle of 60+x degrees with vector b.

I also tried solving with components. I calculated 4N and 7N for the hor. and vert. components of b, respectively and 0N and 15N for the resultant. But after this I am completely lost!

I would really appreciate some feedback just on how I have my diagram set up and maybe some tips on where to go from here, if I have anything correct! Thank you!