Are you talking about the Reagan Dime or a totally different coin? Please start a new separate thread. Pictures are always needed to determine an answer.
You should create a thread with photos as previously mentioned. These old threads don’t attract much attention………. There was once legislation introduced that would have created a US mint issued Reagan dime. That legislation was turned down, so there are no US mint issued Reagan dimes. That means your dime is a tribute piece created by a private mint. The orientation of obverse and reverse that you mentioned is called a medal orientation. And long and short is that a private mint can orient a piece however they desire, and a medal orientation makes sense for a non-circulating tribute piece like you have described.