Provided you actually get measurements on each attempt, of course.
Pick three arbitrary points on a piece of graph paper (well, not completely arbitrary, they shouldn't be on one line). The wider they're spaced, the better resolution you get (prospecting doesn't display fractions, IIRC).
Now go to equivalent points in H&H and prospect. I suggest making it 1mm per tile.
Take the readings and go back to the graph paper. You now need to draw circles centred on those points. Take the readings and multiply them by 10 (1% in prospecting is 10 tiles, if my scouts are to be believed). These are the radii of your circles.
When you draw the circles, they will all intersect in a single point. This is where your mine is. Go near that tile in H&H and use your fourth and final use of extract to put up the mine site.
There are more elegant ways to calculate the position, but this is the one that takes the least math, I think, so it should be doable by anyone.