Closed Triangle of Forces in Equilibrium

When there are three coplanar , concurrent , non collinear forces acting to keep an object in static equilibrium, Lami's Theorem may be used :-

Lami's Theorem

 

Derivation of Lami's Theorem

Using geometric properties:

 

giving alternate angle

then

putting all together :

 

 

which is the vector addition B + A + C

 

Applying the Sine Rule:

but

so

 

Examples using Lami's Theorem

A baby suspended from a doorway jumper is in static equilibrium. Calculate forces x and y.