You're going to want to keep the axes as is, but a quick translation shows that you are correct in assuming the angle.
Now, you may or may not know that the components of the vectors are scalars, represented by for the force in the direction and for the force in the .
We also know that the magnitude of the force (I'll call ), which is 10N, is the hypotenuse of a right triangle, meaning that we can define and in terms of the force:
Because in the unit circle, we define it to be cos = x/hyp.
This means that:
To prove it, we will rederive the magnitude of the force by using the pythagorean theorem, that tells us that:
We know that so we get:
And there you go.
The final statement is: