Solving for Alpha in Mechanics: Trig Formulas and Force Components

[CivilSigma]

So I have a mechanics question 2.65 of which I have deduced the following :
x-Component of all forces
F1 = 150 cos30
F2= 150 cos \alpha
F3 = 150 cos(\alpha+50)

y-Components of all forces
F1 = -150 sin30
F2 = 150 sin \alpha
F3 = 150 cos(50-\alpha)

Finally, R = \sqrt{(\Sigma Fx)^2 + (\Sigma Fy)^2}

Now we know the resultant is at max 600 N, how do we go about solving \alpha ? I tried applying various trig formulas like angle addition and subtraction, but I couldn't isolate \alpha. How would you go about solving for alpha?

 

[mfb]

Set R to 600N, then plug everything in and see what you get (and please write it down here, so we can see where exactly you get stuck).