$(20$ pts$.)$ A $15\mathrm{.}0-kg$ uniform ladder leans against a wall in the atrium of a large hotel. The ladder is $8\mathrm{.}00$ m long; it makes an angle $=60\mathrm{.}0$ with the floor. The coefficient of static friction between the floor and the ladder is ${}_s=0\mathrm{.}45.$ How far along the ladder can a $60\mathrm{.}0-kg$ person climb before the ladder starts to slip? Assume that the wall is frictionless.

Draw F$.$B$.$D of the ladder