3D Equilibrium Statics Problems

[tamara1025]

I'm so stuck on this problem. I got it completely wrong on my test because I don't even know where to start. All i recall is that we mus use the vector approach? The problem states:
For the figure shown, calculate the reactions at point O due to the tensions in the two cables BA and BC. T(BA)=700 N, T(BC)=800 N. Assume that the tree is rigidly fixed to the ground.

 

[pongo38]

Vectors or not, there has to be a similarity between the geometrical triangle OBC and the force components on the cable BC. To get the force components in terms of ijk, you need to project OC onto the x-axis. Let's call it OC'. Then the geometric distances BO, OC', and C'C are in the same ratio as the force components of the 800 N force. There should be as many as 3 reaction components at O that are forces, and three that are moments, although My will be zero by inspection because the forces both seem to pass through it.