The two ropes attached to the hook in the figure below are pulled on with forces of F1 = 150 N and F2 = 300 N. What size single force acting in what direction would produce the same effect?

Question

The two ropes attached to the hook in the figure below are pulled on with forces of F1 = 150 N and F2 = 300 N. What size single force acting in what direction would produce the same effect? 
F1 45 Degrees
F2 30 Degrees

Henry · Answer

F1 = 150 N. @ 45 Deg.
F2 = 300 N. @ 30 Deg.

X = hor. = 150*cos45+300*cos30 = 366 N.
Y = ver. = 150*sin45+300*sin30= 256 N.

tanA=Y/X = 256/366 = 0.6996,
A = 35 Deg.

F = X/cosA = 366/cos35=447 N. @ 35 Deg.