Finding the angle for force component

[TheShehanigan]

Homework Statement

Find the Fx' and Fy components of the given force, given that y' is 10 degrees, there is a 60 degree angle between F and X in the negative direction, and F = 360 N. Use only the Law of Sines, Law of Cosines and Law of Parallelograms.

Homework Equations

Sin a / A = Sin b / B

C^2 = A^2 + B^2 - 2 AB Cos c

Law of Parallelograms for Vectors

The Attempt at a Solution

I've found so far a nice triangle, the one that covers the positive X axis, but I am having trouble finding Phi (which is supposed to be 10). If I can find Phi, I can solve for the components, which I know how to do. Problem is, I'm not told x' and y' are perpendicular, so I can solve using 90 degrees, or anything. I just have the 30 degrees on the bottom, and the 60 + Phi on the top left, but I'm missing the top right. Any tips on finding Phi?

Here's a pic.

 

[LCKurtz]

Could you give the exact statement of the original problem? I suppose the black lines are perpendicular x and y axes, but you haven't labeled them. And you haven't said what x' and y' are nor are they labeled. My guess is that they represent a rotation of the x and y axes through 10 degrees. I would also guess that you have the F vector pointed in the opposite direction if the angle between F and the x-axis is -60 degrees.

Please state the problem, word for word, from where you got it.