Three cables pull on the pipe such that they create a resultant force having magnitude FR. If

Question:

Three cables pull on the pipe such that they create a resultant force having magnitude FR. If two of the cables are subjected to known forces, as shown in the figure, determine the direction θ of the third cable so that the magnitude of force F in this cable 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.
Given:

FR = 900 lb
F1 = 600 lb
F2 = 400 lb
α = 45 deg
β = 30 deg

Three cables pull on the pipe such that they create