Did I do the right thing?

Okay, first off I'd like to pose a question... Here is the situation. Say you work with a girl and she is always saying rude things to people. She has a sexual induendo FOR EVERYTHING and makes sure everyone in the work area can hear her talking in an unprofessional way. If you were in this situation would you tell your boss about this employees behavior?

I am not easily offended unless it comes to religion or politics.. For example my friend at work kept telling me after I had voted for President Obama that I voted for the "Anti-Christ" it really offended me. This same particular person also dogs on religion. Even though this person went on a mission. I respect people's opinions and I hope they respect mine. I am a free thinking 27 year old woman. I have strong beliefs.

Anyway, so the story is this girl at work is very crude in her language and what she says at work. And I finally got sick of hearing it. This particular girl also told me that one of my good friend's cheated on her husband even though I know it's not true because she has been married for over 30 years. I am a good friend and told my friend what was said behind her back. I would like a friend to approach me if someone was bad mouthing me. Come to find out there were 8 people in my area who were also sick of her crude and rude behavior. Well, we all talked to our manager. And my manager talked to her. Well thursday in our team meeting she got up and did a public apology, but then it ended up being a BIG drama fest, she tried to make those of us who had said something feel like crap, because she could have lost her job over this! Well, don't be rude to people and don't talk dirty at work. It's called sexual harrassment and we don't need to deal with it! I am glad that I said something. Because I don't need to listen to it at work of all places!