The document summarizes the solution to a problem involving a rope between two inclines. It finds that: 1) The maximum fraction of rope that can hang in the air, fmax, is approximately 0.172. 2) This occurs when the angle between the inclines, θmax, is 22.5 degrees. 3) The analysis balances the forces on portions of the rope to derive an expression for f in terms of θ, and finds fmax by maximizing this expression.