You've got the right idea, although it sounds like you're just plugging in numbers without being sure about why it works. I'm also not sure how that term under the square root in your first part came out to be positive - it doesn't look like it would, given what you've written.
Look at your second diagram. Can you add the resultant force to it? That should give you a triangle, and the calculations you've done apply directly to that. Keep in mind that the angle you've called theta is an external angle to the triangle, so you have to be careful about how the sine and cosine of that angle change, compared to what you'd get for the internal angle, which is what the sine and cosine laws refer to.
The force diagram - i.e. a picture of real space with the force vectors drawn from the points where they are applied - is your first diagram. After you've used the second diagram to find the magnitude and direction of the resultant force, you can copy it to the first diagram to see how each of the forces acts. You could also have done the whole problem there (which would be my preference), using the parallelogram rule for adding vectors. You get the same triangle as in the second diagram.
I think you've got the right ideas here (and your answers look right to me); you just need to be clearer on why it all works. Keep posting questions until you're sure you've got it.
