Which Method is Correct for Solving Statics Physics Problems?

[frozen7]

I have two different ways to solve this question. The first method is using the method taught in textbook: Draw the parallelogram and bend F to a direction which is perpendicular to the resultant force, and use sine rule to find F.
The second method I use is by assuming the direction of the resultant force of 600N and 400N is parallel to F, hence the resultant force,900N is parallel to 400N and F also. Under this condition, F can only be the minimum. The answer I got from the second method is much smaller than the answer from first method.
Can anyone tell me which one is the correct method? Where did I get wrong??
Thanks in advance.

 

[haynewp]

The question wants you to minimize the force in the cable "F". So in order to do that, you would want to find the angle and magnitude of the resultant of forces given already (like it says to do) then make "F" parallel with this force (at the same angle). So first break apart the given forces into x and y components and find the resultant and its angle.