Explain the proof for lemis theorm

You mean Lami’s Theorem?

Consider the figure. Three concurrent forces net to static equilibrium at the origin. Let's assume for simplicity force a is along the positive x axis.

We have equilibrium when the components of force balance in both dimensions. In particular in the y dimension,

We're free to move our coordinate system around to make any of the force vectors the x axis and then we'd get the same sine balance as in the Law of Sines for the remaining pair of sides.

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