Bucket supported by wood frame and tension wire

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SShep71
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Homework Statement
A 160-lb bucket is suspended from a cable on the wooden frame.

Determine the magnitude of the resultant internal normal force acting on the cross section at E
Determine the magnitude of the resultant internal shear force acting on the cross section at E
Determine the magnitude of the resultant internal bending moment acting on the cross section at E
Relevant Equations
Sum of forces (x and y)
Moment about "E"
Attached is an image of the HW problem, included is a YouTube video I found for a solution.
Assuming the solution shown is correct my question is about the rest of the system. I always approached problems from a top down "total system" perspective. Then try to isolate the portions of the system that are irrelevant for what I am solving. In this problem, the diagonal support for the cantilevered beam "G-H" would carry and transmit a resultant horizontal force into the main vertical member "A-B". Yet this solution and consequently the homework does not address this force. Why is the "x" component of the G-H force ignored?
 
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