When attempting to determine your friction prediction, try the following steps:
1) Draw force diagram
2) Sum forces in x and y directions
3) For x-direction forces, solve for force of friction (this answer will still have a sin A)
4) For y-direction forces, solve for normal force (this answer will still have a cos A)
5) Insert these two answers into the friction equation.
6) Solve for the angle.
7) Use the angle to calculate the minimum height required for the slide.
Good Luck!