Solve Cable Torque Problem: Find Hcomponent Force on 23.8 kg Beam

[Jm4872]

Homework Statement

A 23.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90°. If the beam is inclined at an angle of theta=30.7° with respect to horizontal, what is the horizontal component of the force exerted by the hinge on the beam? (Use the `to the right' as + for the horizontal direction.)

Homework Equations

t=fdsin(theta)

The Attempt at a Solution

I solved for T using torque, however since there was no length of the beam given I assumed a length of 2 meters so that i could find tension using the equation :
-mg*1m*sin(30.7)+T*(2m)*sin90=0
T=111.7 N

Then I solved for the horizontal component of the force from the wall using the following equation :
-Tcos45+Hcomponent=0
therefore Hcomponent = Tcos45

And this is not right, can anyone explain to me what I've done wrong, I'm so confused ??

 

[Delphi51]

-mg*1m*sin(30.7)+T*(2m)*sin90=0
T=111.7 N

It seems to me it should be cos(30.7) instead of sine.
The assumption of 2 m length does no harm - length cancels out anyway.

-Tcos45+Hcomponent=0

Why 45 degrees? Why cos? Carefully draw the diagram and carefully figure out that angle!