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Thepotemich [5.8K]
3 years ago
8

Explain the Proof for Lemis Theorm

Mathematics
1 answer:
11111nata11111 [884]3 years ago
3 0

You mean Lami’s Theorem?


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


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


b \sin C = c \sin B


\dfrac{b}{\sin B} = \dfrac{c}{\sin C}


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.


\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}



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