You are given one force: 300 lbs acting in the C to A direction (the angle is given). You need to find out what force, acting in the B to A direction, that when added to the first force gives a resultant equal to 500 lbs.
Call the unknown force F. Now add the two forces (by adding their components). Set the magnitude of the resultant equal to 500 lbs to solve for F.
You find the component for the force along BA the same way you found the components for the force along CA. The difference is that you don't know the magnitude of the BA force, but that's what you will solve for. Call the magnitude of that unknown BA force "F" (or some other symbol of your choice).
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