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How to use "-한 면이"? Thank you!

"~한면이 있다" in your sentence means someone "has a characteristic of ~" or in other situations, something “has an aspect of ~”

So, the direct translation of 터프한 면이 있는 사람 would be "a person who has a characteristic of being tough." Simply put, "a tough person." 터프한 면이 있는 사람이란 걸 알게 됐어요 would directly translate to "I got to know that he is a person who has a characteristic of being tough = I found out he’s tough.”

We use ~한면이 있다 in the following ways:

너가 꼼꼼한 면이 있는지 몰랐어: I didn't know you had a characteristic of being detail-oriented = I didn’t know you’re detail-oriented.
너가 그러한 (그런) 면이 있는지 알게 되었어: I got to know that you have that characteristic = I found out that you’re like that.