"That woman is famous."
That may be ok that time but would respectfully recommend not relying on google translate. It can so often be incorrect and particularly in its english with that of britain. The same issue for spelling many words and syntax where appropriate too. By far more reliable with book dictionary or thesaurus etc with any foreign language in question based on british english translation for those in England.
Thanks for that. I was going to ask what context this would appear in, since if "that woman" is その rather than あの, it should mean she's close to the person you're speaking to, which made me think it would be rather rude to talk about her in the third person like she can't hear you.
In case you're still looking for an answer:
女 and 男 are plain forms by themselves. They are casual to the point of being downright derogatory, especially when used to talking about other people. This is why it's only okay to use them by themselves when talking about yourself, because it's very clear that you are speaking plainly and not implying anything derogatory/offensive.
男の人 and 女の人 are both more neutral, polite forms. You can think as the first kanji only denoting sex, while the second denotes a person (as opposed to reducing them to their genitals)