MSU has an article explaining the difference between a zoning map and a master plan.
Bascially: the master plan explains goals for our community, and what we'd like to do, but it's the zoning map that is the actual law. Even when the planning process requires review against the master plan, my understanding is that that review is mostly just advisory. If the project otherwise meets zoning and code, it probably can't be rejected just because of the master plan.
Ann Arbor's master plan is actually a collection of documents; see the City Master Plan page for links.
You can look at the zoning map here. Or, there are more ways to get it (like as pdfs) on the city's zoning administration page. If you just want to look up the zoning of a single property, simplest is probably to a "properties" search on etrakit.
But then you need to know what the zones mean. The definitive reference for that is the code.