# 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:

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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...!