Beam hinged to wall at 30°, supported by cable 2 m from end

[srhhhla]

Homework Statement

A uniform 8 m 1500 kg beam is hinged to a wall and supported by a thin cable attached 2 m from the free end of the beam as shown in the figure. The beam is supported at an angle of 30 degrees above the horizontal.
a) free diagram
b) find the tension in the cable
c) how hard does the beam push inward on the wall?

Homework Equations

net torque = 0 / net force (x) = 0 / net force (y) =0

The Attempt at a Solution

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[rl.bhat]

Let T be the tension in the string.
Resolve it into two components.
One perpendicular to beam, and another along the beam.
Resolve the weight of the beam into two components.
One perpendicular to beam, and another along the beam.
In the equilibrium position, equate the torque due to the components of weight and the tension and find T.
For part c) add the components of weight and the tension along the beam.