Unfortunately, it's not really simple enough to slap a calculator on it.
If you wanted to know what stress level is acceptable for a straight beam, without any bends, with no holes in it... Well, that's simple enough and could easily be made into an online calculator. Then it'd just be a matter of figuring out if that stress level is below the acceptable stress levels- either by failure from yield, fatigue, or unacceptable deflection.
BUT- as soon as you throw in some more complicated geometry, for example a hole, bend, or weld... It quickly becomes too complicated to be easily solved by a casual observer.
You will either need to do significant research, or- more practically- find something somebody else already engineered that does the same thing, and copy / modify that design, making it "robust".
Sorry there's no easy way out-
PS: Just looked at your example... Just go look at a small crane or something that will lift loads at an angle similar to that. The worst case scenario will probably be with the boom all the way extended. Remember that if you set up the cable like that, the cable is also pulling down on that boom, so the weight lifted is effectively multiplied by some number, from probably 130-170%, depending on the geometry.
Remember that your trailer needs to be strong enough to absorb the entire weight of the load and then quite a bit, all in one spot (your mounting spot for the boom).
Keeping the boom from rotating will take some serious force / torque.