Dave, if you can see the tangent line while behind the cueball, why can't you see the aiming line and go down on that line and shoot ?
Because it's approximated when standing at the CB. I'm not approximating my aim from the CB. Even after I lock into the shot solution, it's still tough to see the exact tangent line from the CB. I'm not even sure it really matters since most of the time you're not going to have perfect stun on the CB to hit the tangent line exactly anyways--- the majority of the time you're hitting the CB with high/low.
I'm not saying the tangent line doesn't matter--- it does... it's just that knowing it exactly (from the CB) isn't really needed in most circumstances.