$[2.](25$ pts$)$ You open a restaurant and hope to entice customers by hanging out a sign as shown in the figure below.

The uniform horizontal beam supporting the sign has a length of $L=1\mathrm{.}50m,$ has a weight of $157$ N $,$ and is hinged to the wall.

The cable makes an angle of $=41\mathrm{.}4$ with the beam, as shown.

The sign itself is uniform with a weight of $274$ N $.$

The two wires supporting the sign are $d=0\mathrm{.}900m$ apart, and are equally spaced from the middle of the sign.

$($a$)$ Find the tension $T$ in the cable.

$($b$)$ Find the reaction force $($magnitude and direction$)$ exerted on the left end of the beam by the hinge.

Hint: The weight of the sign $($call it $W_s)$ acts at the CG of the sign. Call the lever arm for the sign $x.$

You know $L$ and $d,$ so you can easily calculate the lever arm for $W_{s.}.$