truss structure geometry - geometric induction? This might be a really simple Geometry rule that I'm missing, but I can't understand how in this problem they automatically knew to extend the truss to point X and knew that it was an additional 2 little triangles. I know that if I were to solve the entire truss using the typical tools like law of sines/cosines, and pythagorus, I could perhaps conclude the same thing, but it seems like there is a big shortcut I am missing to do this instantly. attached are print screens from Meriam & Kraige Statics textbook of the problem and the solution: !The problem !Solution

I think that what they did here is a standard "trick" used a lot in geometry-trigonometry problems: they draw a a help-line (or help-circle or whatever) in order to make the problem easier and/or more manageable.

In the present case, they extend in a straight way the line FJ from the side of J all the way until it meets in point X the straight extension of line OL in order to form the straight-angle triangle $\,\Delta FOX\,$, with $\,\angle FOX=90\,$ , and **now** they can use trigonometric functions to do stuff...!