Why Is My Calculation of Force Along a Line Incorrect in Statics?

[vineroon]

I have been having trouble with this seemingly easy problem. You would think that it is just as simple as finding Fcos(tan^-1(3/4)), which yields the answer 320 N. However, as seen in the image, the actual answer is 420 N.

I would appreciate any help.

Thanks

 

[PhanthomJay]

You've calculated the x component of the given force. That's not what the problem is asking. You need to calculate the x and y components of the forces AB and CD, then set the sum of those x or y components equal to the x or y components, respectively, of the given force.