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Solution

For this problem, we first generate values for the lever arms:

Fa Lever Arm: SinA = x/5.2 m
(SinA)(5.2 m) = x

Fg Lever Arm: CosA = x/2.6 m
(CosA)(2.6 m) = x

We also need the value of Fa, which we know must equal Ff in order to solve. We know the coefficient of static friction and we know that the normal force must equal the total Fg force so it must equal 90 N. Therefore:

Coefficient of Static Friction = Ff/Fn
0.61 = Ff/90 N
54.9 N = Ff = Fa

Now keeping in mind that the ladder is in equilibrium, we can write the following equation and solve for the missing angle A value.

Torque CW = Torque CCW
(CosA)(2.6 m)(90 N) = (SinA)(5.2 m)(54.9 N)
234 = (TanA)(285.5)
0.82 = TanA
39 degrees = A