LAMI'S THEOREM CONCEPT

It states that "If there forces acting at a point are in equilibrium, each force will be proportional to the sine of the angle between the other two  forces."

If the three forces P,Q and R are acting at a point A and they are in equilibrium as shown in below in fig.1

Let us consider,       α = Angle between force P and Q
                                    β = Angle between force Q and P
                                    γ = Angle between force R and P

According to Lami's Theorem,
P α sine of angle between Q and R α sin β.

           
                 ∴           

Similarly,                           

and

.

or equation can be written as

               ......equation 1

Proof of Lami's Theorem

The three forces P,Q and R acting on a point A,  are in equilibrium position and they can be represented by the three sides of the triangle taken in the same order.

The force triangle as shown in Fig.2

We apply sine rule on fig.1. we get equation in the given below.

this equation also written as

                         ......equation 2

Now equation 1, 2 same. So Lami's Theorem verified.