If you are in the right, what you are doing is morally or legally correct.

You're definitely in the right - there's no doubt about that.

They felt they were in the right.

I felt justified in saying what I said because I knew I was in the right.

She's convinced she's in the right and nothing I say will dissuade her from that view.

So who's in the right here?

I think David is in the right on this one.

See also: right noun (MORALLY ACCEPTABLE)