Solving Hanging Sign Problem: Find Tension, Horizontal & Vertical Force

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The discussion centers on calculating the tension in a guy wire supporting a shop sign and the forces exerted by the hinge on a beam. A sign weighing 206 N is supported by a 132 N beam, with the guy wire connected at a distance of 1.19 m from the backboard and at an angle of 43 degrees. The initial calculations presented for tension and forces are deemed incorrect due to mismatched units and improper torque considerations. Participants emphasize the importance of correctly identifying the forces and their points of action to solve the problem accurately. The conversation highlights the need for clarity in applying physics principles to avoid confusion in calculations.
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A shop sign weighing 206 N is supported by a uniform 132 N beam of length L = 1.89 m as shown in figure below.

The guy wire is connected D = 1.19 m from the backboard. Find the tension in the guy wire. Assume theta = 43.0 o
Find the horizontal force exerted by the hinge on the beam.
Find the vertical force exerted by the hinge on the beam. Use "up" as the positive direction.

I get T = -mg * 1/2L + T*L*sin(43) = T = mg/2sin(40)

Fx = Hx -T cos(43) = 0
Hx = T cos(43)
Fy = Hy -mg + Tsin(43) = 0
Hy = mg - Tsin(43)

But these are incorrect. Where did I go wrong?
 

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"I get T = -mg * 1/2L + T*L*sin(43) = T = mg/2sin(40)"

This is complete nonsense!

You have 3 forces creating torques about the hinge. Which, and where do they act?
 
That wasn't suppose to be torque but rather tension.
 
It's still nonsense, since your units don't match (T and TL have not the same units)
 
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