No idea what 'the problem' is, but the solution involves trigonometry. And the steel bible. I recommend taking a statics class, it's not rocket science.

I don't see a specific question, but in general, it's a torque problem, acting relative to the pivot point--the lower connection at the wall. (Torque is force times distance; units typically ft•lbs or Newtons.) In the counterclockwise direction you have the force pulling down times the distance to the pivot point. Acting in the other direction is the tension load in the cable; that distance is measured from the pivot point to the point on the cable perpendicular to the pivot point. The two torques have to cancel each other out, so force times distance of one equals force times distance in the other.

Once you know the tension load in the cable, you can resolve it to its vertical and horizontal components, which happens to relate proportionately to the dimensions of the triangular shape you are analyzing.

I would hire a structural engineer and let him take the liability. 

that has nothing to do with torque.  wood guy has no idea what he is talking about.

"how would you crack this problem?"

Ask archinect of course! Can you transfer liability to a website though?

Just use the side of the pan like you would with an egg.

Chigurgh, you're funny. I have a BS in engineering (90% of a civil/structural degree as part of a pre-arch program) and know exactly what I'm talking about. Sure, you can just apply trigonometry and get an answer, but the way I learned to visualize what was happening in a problem like that is to resolve the forces using torque equations. The question was "how would you crack this problem." If architects need to call an engineer to understand the forces in a simple diagram like that, that is sad. 

I would start by mirroring the text so I could read it more legibly

RVTS, here is a decent video solving your problem using classic statics techniques: https://www.youtube.com/watch?v=dbjNX91EQh0&t=18s.

Here's one using torque to actually visualize what is happening: https://www.youtube.com/watch?v=V_lxELlEOFg.

Unless you're a geometry wiz, there's nothing much intuitive about the first approach, though it should be simple enough once you learn the principles. I'm a visual learner and the concept of torque (which, again, is simply force times distance) makes more sense to me. 

First I'd go find the textbook, so I could see the problem in a not-blurry and not-backwards manner.  Then I'd read the book, and do my homework.

I would call my structural engineer.

 To the regulars here, let's not forget the OP's already stated in previous posts that he's a structural wizard and will force the entire shut-down of US construction via strike among many other things.

I would solve the problem by sending it to my engineer.  

Do your homework.

Wood guy is close; it's a moment arm type problem.  So the horizontal is pushing against the wall (where the moment radius starts), the top arm is trying to pull out.  So you use 'geometry' and vector forces to figure out the loads and size everything correctly.

It's highschool level physics & geometry.  So if you can't solve this, you really need an engineer.  Simple overkill if in a rush: if it's 1000# hanging on a 3' horizontal, figure 3000# pullout at the top (3x1000), and 3000# push on the wall at the horizontal.  Also don't forget that wall you are connecting to is also going to want to rotate now, so it needs to be designed for it.

how much harder than statics is rocket science ?

^ Plagiarized from "Cracking A Problem:  Another Use for a Fashionable, New Materials", The Economist, 2011.

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The force is dependent of the weight on the end of the beam and the angle the smaller beam, or cable, makes with the horizontal beam. Oddly enough, the length of the horizontal beam is not a factor.