Up until the moment the box starts to slip, the static friction is maximized with magnitude f, so that by Newton's second law,
• the net force acting on the box parallel to the ramp is
∑ F = mg sin(α) - f = 0
where mg sin(α) is the magnitude of the parallel component of the box's weight; and
• the net force acting perpendicular to the ramp is
∑ F = n - mg cos(α) = 0
where n is the magnitude of the normal force and mg cos(α) is the magnitude of the perpendicular component of weight.
From the second equation we have
n = mg cos(α)
and f = µn = µmg cos(α), where µ is the coefficient of static friction. Substituting these into the first equation gives us
mg sin(α) = µmg cos(α) ==> µ = tan(α) ==> α = arctan(0.35) ≈ 19.3°