Applying Parallelogram Law in Mechanics

If you have a force system like this as shown in figure XY1-1, you have to analyse it and redraw it just like in figure XY1-2.

XY1-1

XY1-2

Two forces A and B add according to parallelogram law, yielding a resultant force C that forms the diagonal of the parallelogram.

get the other half of the parallelogram and redraw just like in figure XY1-3.

XY1-3

you may solve for the unknown values using cosine law:

and using sine law: