Question

A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is μ1 = 0.195 and the coefficient of friction between the ladder and the wall is μ2 = 0.253. Determine the maximum angle with the vertical the ladder can make without falling on the ground.

Answer 1

Here:
Sum Fx| Fgx=Fw
SumFy| Fgy=mg-mu2xFw
SumTorques | Fw(Lcos(theta))=mg(L/2)sin(theta) - Now,this leads to-->Fw=Fg=(mg)/(2tan(theta))For no slipping Fgx<=mu1(Fgy)

Just make the substitutions and it gets ugly but the final thing you get should be 

theta= arctan[(1-mu1x mu2)/(2mu1)) , which equals 67.946 then subtract from 90 and viola!
you get the answer of 22.305