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to meet with (misfortune); to encounter (something unpleasant); to experience (an accident, disaster); to undergo; to suffer
to have an accident; to have a bad experience
災難に遭ってしまった。
I met with a disaster.
不運にも交通事故に遭ってしまって入院した。
I got into a traffic accident.
旅行中にひどい嵐に遭った。
I encountered a terrible storm during the trip.