Problem $3(25$ points$)$:

A ladder supports the $80-kg$ man in the position as shown in Fig. $3.$ The surface is rather slippery, where the coefficient of static friction at A and $B$ is ${}_s=0\mathrm{.}25.$ Fortunately, an invisible guy helps hold the ladder $BC,$ providing a couple moment shown in the figure.

$($a$)$ Draw the free body diagram of AC and BC $,$ respectively. $(5\%)$

$($b$)$ Determine the greatest angle $$ so that the ladder does not slip under this condition. Start by assuming the ladder slips at $A.(20\%)$