Draw a line through the center of the hole, following the path of the drill.  Draw two lines from a point P on the lip of the hole, one a perpendicular to the drill path and intersecting at point D and one to the center of the ball (C).  CPD is a right triangle, with CP = 13/2 and DP = 5/2.  This is half of a 5-12-13 right triangle, so CD = 12/2.  Double this to get the height of the hole, top to bottom.