A light stool in the shape of an equilateral triangle has three identical vertical legs A,B,C at the corners and sits above a horizontal ground. Choose a coordinate system and length scale so that...

A light stool in the shape of an equilateral triangle has three identical vertical legs at the corners
and sits above horizontal ground. We choose a coordinate system so that the floor coincides with
the xy-plane and the points where each leg makes contact with the floor are
     0, 1,0 , 0,1,0 , and 3,0,0 .A B C The height of the stool is h. A mass m is placed on the
stool at the point  , , .M x y h We wish to compute the force through each leg supporting the mass
in terms of x, y, g, and m.
Let AF , BF , and CF be the forces through the legs in contact with the floor at the points A, B, and
C respectively. Since these three forces are supporting the mass m, we have
.A B C m   F F F g
Now since each of these three forces acts in the +z-direction, we have
.A B CF F F mg  
Since the mass on the stool is in static equilibrium, the net torque acting on it must be zero. Thus
we have
.A B C  τ τ τ 0
Now we have
   
  
,...