Sacrifice - Mate in 3!

yes shows the importance of never assuming your opponent will do what you want/expect him or her do. In no way was black forced to take the rook.

White's best move (objectively) from the starting position is clearly Rxb4.
After Rxg5, with correct play black should clearly win. For example:
1. Rxg5 Bxd2+
2. Kf1 Bc3
3. Qc1 Rd1+
4. Qxd1 Qxh1+
5. Rg1 b4+
6. Qd3 Bxd3+
7. cxd3 Qh3+
8. Ke2 Qh5+
9. f3 Qh2+
10. Kf1 Nh4
11. d4 Qd2
12. Rg8+ Kf7
13. Rg7+ Kxg7
14. Kg1 Qg2#
Have fun!