Finding Angles of Interacting Forces

[gajohnson]

Homework Statement

http://grab.by/lp4S

This probably shouldn't be too hard, but I'm getting pretty stuck. On the attached picture, the angles 67.4 and 22.6 are given, but I am not sure how they were found. Taking all the given information on the picture (besides those two angles), how would I find them? I think my trig is just rusty and there's probably an easy solution.

Homework Equations

The Attempt at a Solution

I tried to create a force triangle and use the law of cosines and to get F(BD), but that didn't work out, and I'm sort of stuck otherwise. Any help would be greatly appreciated. Thanks!

 

[haruspex]

From the picture, it seems you would have three unknowns: the magnitudes of forces F_BC and F_BD, and the direction of F_BD. Resolving in two axes will only give you two equations, so there's not enough information to deduce the angle.
Where it says "since the direction of F_BD is not clear", I think it only means the sense is unclear - i.e. is it positive or negative in the direction shown? For the purposes of solving the problem, just assume a particular sense and see what sign you get from the solution.