Find the components for F (AC)?

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To solve for the unknown force F acting from B to A, start by identifying the components of the known force of 300 lbs from C to A using trigonometry based on the given angle. Next, combine this force with the unknown force F, ensuring the resultant equals 500 lbs. Use the same trigonometric methods to find the components of F along BA as you did for CA. The key is to set up the equation with the magnitudes of both forces and solve for F. This approach will yield the necessary components for both forces to achieve the desired resultant.
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I don't know how to start off. What steps do I have to take to solve this problem? I am completely lost.
 

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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.
 
I have to find the components for F (AC)?
 
You need to find the components of both forces. But you are given the angles, so use some trig.
 
I am able to find the components for AC but how do I get the components for AB using the angles? Is there a formula for it?
 
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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