Solving for the Reaction Force by taking Moment about a Point

[daisy7777]

Homework Statement

The stiff-leg derrick used on ships is supported by a
ball-and-socket joint at D and two cables BA and BC. The
cables are attached to a smooth collar ring at B, which allows
rotation of the derrick about z axis. If the derrick supports a
crate having a mass of 200 kg, determine the tension in the
cables and the x, y, z components of reaction at D.

Relevant Equations

∑Fx=0; ∑Fy=0; ∑M=0; ∑Fz=0;

For this problem, I took the moment about point B to 'get rid' of the tension force in the cables BA and BC. By doing this, I figured I could solve for the x and y components of the reaction force at D. From there, I could solve for the tension in BA and BC in the x and y and then solve for Dz. However, I got the wrong answer doing this and when looking at a video they approached the problem by taking the moment at D and solving for the tension in both the cables from there. Was my approach wrong or did I simply make a mistake in my calculations?

 

[erobz]

Please share your work in a clear format (preferably using LaTeX Guide) ,and maybe we can figure out what happened. I have suspicion that you neglected the tensions and/or reaction at $D$ in the rigging attached to the mast when taking your moment about $B$. In other words perhaps we should examine what you think is a FBD of the mast. Maybe you made no mistake in the physics and just have a math error (maybe position vector from $B$ to the tip of the boom). I can't tell.

There is nothing wrong with taking torques about $B$ in theory to get some equations. Maybe it's a shortcut ( I assume you think it is). It could be nothing special though too.