Original post by ghostwalkerCouple of options:
Assuming the underlying coal lies in a plane, using Da for the depth at A, etc. you have:
Db-Dc = Da-Dd
This works because you have a rectangular grid.
However if that is too terse and assumes too much, you'll need to use the equation of a plane. Equally if you get a question where the grid isn't rectangular, nor something else nice, you'll need this method.
So slap a set of co-ordinates on the grid - I'd base it at D.
Then at any point the depth is givan by H = ax + by +c, where a,b,c constants, as yet unknown, H is the depth of the coal at the hole, and x,y are the co-ordinates of the hole.
Set up three equations for the three known holes, and solve. You're only interested in the value of c, as that will be the depth as the origin, the hole D.