Three chains act on the bracket such that they create a resultant force having magnitude FR. If

Question:

Three chains act on the bracket such that they create a resultant force having magnitude FR. If two of the chains are subjected to known forces, as shown, determine the orientation θ of the third chain, measured clockwise from the positive x axis, so that the magnitude of force F in this chain is a minimum. All forces lie in the x-y plane. What is the magnitude of F? Hint: First find the resultant of the two known forces. Force F acts in this direction.
Given:

FR = 500 lb
F1 = 200 lb
F2 = 300 lb
φ = 30 deg

F2 F1