Acceptance With Displeasure. It's possible that your boss won't take immediate action like the reaction above__but will make it clear that he or she isn't exactly happy about your resignation. Maybe, for example, she'll mutter a curt, "Thank you for letting me know," followed by two weeks of obvious displeasure or denial that you're leaving__through gruff comments ("You know, you're really leaving us in the lurch") or a refusal to interact with you more than absolutely necessary.
Even if you're not close with your boss, chances are you have a working, first_name_basis relationship. Maintaining that in your official letter is okay. You don't need to keep a Victorian level of formality here__just make sure it's a professional tone.