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To solve this problem, we apply the concepts related to the sum of forces and balance in a diagram that will be attached, in order to identify the behavior, direction and sense of the forces. The objective is to find an expression that is in terms of the mass, the angle, the coefficient of friction and the length that allows us to identify when the ladder begins to slip. For equilibrium of the ladder we have,
Now we have that
And for equilibrium of the two forces we have finally
Rearranging to find the distance,
So if we have that the frictional force is equivalent to
With this value we have that
Therefore can go around to 5.19m before the ladder begins to slip.
