Determining magnitude and direction of vectors

[savva]

Homework Statement

Determine the magnitude and direction θ of F1 so that the resultant force is directed vertically upward and has a magnitude of 800N.

Homework Equations

F1=FR-F2-F3

The Attempt at a Solution

I have attached the question with diagram and my attempt at solving the question. I know that by using the equation above, F1=FR-F2-F3, however I am slightly confused as to obtaining the values for these vectors and how to approach doing that.

 

[Joffan]

Solve for F_1x using the horizontal components, solve for F_1y using vertical components, then take F_1x and F_1y to solve for F₁ and θ

 

[savva]

Thanks for your help Joffran, I managed to solve the problem with your help, I will add the working I used to solve it tomorrow

 

[savva]

$\Sigma$Fx=0 ----> 400cos30+F1x-(4/5)(600)=0 ----> F1x=133.6N
$\Sigma$Fy=800 ----> 400sin30+F1y+(3/5)(600)=800 ----> F1y=240N

F1= (F1x^2+F2y^2)^.5 = (133.6^2+240^2)^.5=274.7N

tanθ=F1x/F1y=133.6/240

θ=tan^-1(133.6/240)=29.1