What is proof of lamis theorm?

Answer 1

Lami's theorem states that if three concurrent forces act on a body keeping it in Equilibrium, then each force is proportional to the sine of the angle between the other two forces.

Let P, Q and R be the three forces acting at a point O.

Since OP, OQ and OR are vectors, they can be arranged "nose to tail". Then since the forces are in equilibrium, they form a closed triangle.

Applying the sine rule to the triangle, P/sin[pi - angle(QOR)] = Q/sin[pi- angle(ROP)] = R/sin[pi- angle(POQ)]

Then, since sin(pi - x) = sin(x)

P/sin[angle(QOR)] = Q/sin[angle(ROP)] = R/sin[angle(POQ)]