30-60-90 Right Triangle: Side Ratios

A board $64$ inches long and $4$ inches thick is inclined so that the long side of the board makes a $30$ degree angle with the ground. The distance from the ground to the highest point on the board can be expressed in the form $a+b\sqrt{c}$ where $a,b,c$ are positive integers and $c$ is not divisible by the square of any prime. What is $a+b+c$?

Source: 2011-2012 Winter Online Math Open