What are the magnitudes of the two force components?

[Ryuk1990]

Homework Statement

There is a resultant force going towards the positive x-axis at 500 lbf. Force 1 is going 45 degrees above the positive x axis. Force 2 is going 30 degrees below the positive x axis. What are magnitudes of Force 1 and Force 2?

The Attempt at a Solution

I wrote up equations for total Force X and total Force Y.

Force X: F1*sin45 + F2*cos30 = 500

Force Y: F1*sin45 - F2*sin30 = 0

So from Force X, I know that F1 = (500 - F2*cos30)/sin45.

I applied that to Force Y so [(500 - F2 *cos30)/sin45] * sin45 = F2 sin30

I got totally confused at this point and I have no idea what to do. Am I even setting this up right?

 

[PhanthomJay]

That equation looks OK...you need to solve it for F2, and once F2 is known, solve for F1. You did the physics part...now it's just algebra. Rather than use the substitution method to solve for 2 equations with 2 unknowns, it might be easier to use the 'elimination of variables' method to solve for F2 by subtracting the 2nd equation from the first, which eliminates the F1 term, and allows you to solve for F2 fairly simply.