This is the 12268th most frequent Korean word.
다쳤다고
"다쳤다고" means "said [someone] got hurt" or "said [someone] was injured."
The word '다쳤다고' is used to convey that someone reported or claimed he was injured.
그가 다쳤다고 해서 병원으로 데려갔어요.
They said he was injured, so we took him to the hospital.
Here, '다쳤다고' refers to the reported state of the injury, implying its non-disclosure.
다쳤다고 말하지 않아서 아무도 몰랐어요.
Since you didn't mention you were injured, no one knew about it.
In this sentence, '다쳤다고' introduces information relayed about someone being injured.