How negative sign appeared out of nowhere?

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The discussion centers on the confusion surrounding the calculation of resultant forces in a problem involving couples. A participant points out an inconsistency in the vertical and horizontal components of the forces, specifically noting that the vertical component was incorrectly written as 4/3 F instead of 4/5 F. The mention of negative signs in the resultant force calculation, specifically -2*(4F/5), raises questions about the reference point for moments. Clarification is sought on which point is being used to take moments in the analysis. Accurate component resolution is crucial for understanding the resultant forces in this context.
Benjamin_harsh
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Homework Statement
Determine the required magnitude of force F in the resultant couple
moment on the frame is 200 lb.ft clockwise.
Relevant Equations
##\Sigma F_x = \textbf{-}2*\frac{4F}{5}##
I have to find resultant for this couples:

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My sir resolved given forces into components like this:

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He considered Fx couples for sides 3,4,5 triangles:

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He wrote resultant force for this above diagram: ##\Sigma F_x = \textbf{-}2*\frac{4F}{5}##
 
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You appear to have written the vertical component as 4/3 F, twice, instead of 4/5, and the horizontal once as 4/3 instead of 3/5.

Which point are you taking moments about?
 

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