A Uniform Beam Supported by a Cable

[ginza88]

Homework Statement

A uniform 250 kg beam is supported by a cable connected to the ceiling, as shown in the figure. The lower end of the beam rests on a rough, horizontal floor. What is the magnitude of the tension in this cable?

Image of the problem:
http://session.masteringphysics.com/problemAsset/1026378/6/yg.10.70.jpg

Homework Equations

Fnet=ma=0

The Attempt at a Solution

I know that this problem is easiest to complete using torques, but I was told to try it without using torque (if possible). That being said, here is my attempt:

http://imgur.com/jKr3tDC

I know that I got the right answer but I am not sure how. Aren't the 40 degrees and the 20 degrees are the wrong angles to use when using a horizontal/vertically oriented plane?

 

[haruspex]

Your working does indeed look wrong.
You show the tension resolving into T cos(20^o) horizontally and T sin(20^o) vertically, whereas the cable makes an angle 60^o to the horizontal.
You don't show any frictional force at the ground, but there must be one.