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A ladder of length L and weight W rests against a wall. The coefficient of static friction between the ladder and the floor and between the ladder and the wall is mu=0.5 What is the minimum angle the ladder can make with the floor (theta) without slipping?

What i know:

sum of torques = 0

sum of forces in y dir = 0

sum of forces in x dir = 0

forces in y dir = normal force from floor, friction with wall (mu times normal force from wall),and weight (W)

forces in x dir = friction with floor (mu times normal force from floor), normal force from wall

I have set the torque point at the ladder's contact with the floor and know there will be five equations to deal with.

If anyone could help me find these equations or help me set the problem up i'd appreciate it.

Jeff