Those numbers are correct but there's a simpler way to figure it out. The sides of any congruent right trangle (equal sides and a hypotinuse) are in the ratio 1:1:sqrt 2.

So if the hole is drilled on a 45 degree angle (and assuming the surface around the hole is flat and the vein is virtually straight down) you simply divide the length of the hole by the square root of 2.

However if the quartz vein is also on an angle, and not straight down, it would be impossible to know for sure without seeing the core.