Calculating Resultant Force: Comparing Methods and Identifying Errors

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vipertongn
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Ok so I have something like this...not drawn to scale

http://i53.tinypic.com/303l5k6.gif

I can see that with the law of cos I can get 49N

However...with this other method where you set Sum of F=0

With sqrt(Fx^2+Fy^2)=R

sqrt((40*cos(20)+20*cos(30))^2+(40*sin(20)-20*sin(30))^2)

I get 55N

Is there soemthing wrong? I'm pretty sure the first answer is correct...but I don't know why this one isnt...
 

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The second one looks right, so I'm guessing the first is wrong... what do you mean using the law of cos?

I think the best way is to just break down each force vector into its x and y components; add those to find the resultant, then use the Pythagorean theorem to find the magnitude of the resultant (that's effectively what you did with your second method).