Applied Mechanics and Graphic Statics
Lami's theorem states that

Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
Three forces acting at a point are always in equilibrium

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Applied Mechanics and Graphic Statics
A body of weight ‘w’ placed on an inclined plane is acted upon by a force ‘P’ parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is ‘θ’ and angle of friction is ‘φ’, the minimum value of ‘P’, is

w cos (θ + φ)/cos φ
w sinθ cos(θ - φ)/sin φ
w sin (φ - θ)/cos φ
w sin (θ - φ)/cos φ

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