Verified answer

Assume that the box has a mass of m. First, find the component of gravitational force that acts parallel to the surface of the ramp. It will be equal to mg*sinθ, where θ is 27 degrees. Then find the component of gravitational force that acts perpendicular to the surface of the ramp, which is mg*cosθ. This is also the normal force, so the force of friction will be μmg*cosθ, where μ is the unknown coefficient of kinetic friction. The total force on the box, acting downwards, parallel to the surface of the ramp, is mg*sinθ - μmg*cosθ. Divide that by m, the mass of the box, to find that the box's acceleration is g*sinθ - μg*cosθ. Set that equal to 1.11 m/s^2 and solve for μ to get your answer.