A $20-$ft ladder weighing $70$ lb $($assumed concentrated at its mid$-$length$)$ rests on a vertical plane with its lower end on a horizontal floor and its upper end against a vertical wall The ladder supports a $180-$lb person at the top $($upper end$).$ The coefficient of static friction at the floor and at the wall is $0\mathrm{.}25.$ Please do the following: $3.$ a$)$ Find the smallest angle that the ladder can make with the floor before slipping egins Find the frictional force fbetween the floor and the lower end of the ladder b$)$