Answer:
  μ = 0.336
Explanation:
We will work on this exercise with the expressions of transactional and rotational equilibrium.
Let's start with rotational balance, for this we set a reference system at the top of the ladder, where it touches the wall and we will assign as positive the anti-clockwise direction of rotation
           fr L sin θ - W L / 2 cos θ - W_painter 0.3 L cos θ  = 0
           fr sin θ  - cos θ  (W / 2 + 0,3 W_painter) = 0
           fr = cotan θ  (W / 2 + 0,3 W_painter)
Now let's write the equilibrium translation equation
      
X axis
         F1 - fr = 0
         F1 = fr
the friction force has the expression
        fr = μ N
Y Axis
        N - W - W_painter = 0
        N = W + W_painter
        
we substitute
       fr = μ (W + W_painter)
we substitute in the endowment equilibrium equation
      μ (W + W_painter) = cotan θ  (W / 2 + 0,3 W_painter)
       μ = cotan θ (W / 2 + 0,3 W_painter) / (W + W_painter)
we substitute the values they give
       μ = cotan θ  (12/2 + 0.3 55) / (12 + 55)
       μ = cotan θ  (22.5 / 67)
       μ = cotan tea (0.336)
To finish the problem, we must indicate the angle of the staircase or catcher data to find the angle, if we assume that the angle is tea = 45
        cotan 45 = 1 / tan 45 = 1
the result is
     μ = 0.336