"TO DO LIST" problem 5

In the "TO DO LIST" problem 5, I was really impressed by the way white was able to trap the knight, making it completely out of play and black had to sac a pawn to get it out although by that time it was too little too late. But as much as I was impressed, I feel like I couldn't do something like that, sacing the a-pawn to trap the black knight because I'm pretty materialistic and I don't normally sac pieces without knowing for certain it was going to work out, and at the move Nxa3 I don't think I would have been able to calculate it all out and be comfortable with sacing the a-pawn because even though the knight is out of play, white's B can't really move either (even though it's on a really good square) or else the knight would get out. I wonder if the player was able to calculate it out or just know intuitively from experience (and good endgame knowledge) that it would work out. I guess that's why I'm taking this course. Anyway, I'm curious to see what you guys feel about the position and just sacing material for advantages in general.