Translation:The rich American man is in the study.
I think that would be more adequately translated with műhely ("work-place").
Or yet another suggestion: "office room". I first hear of a room called just "study" :)
"study" and "office" are correct in English. No one says "study room" or "office room.
I'd translate dolgozó rather as "working", but yes, your analysis is right. :)
(-ó/-ő forms the present participle of a verb: nevet - to laugh, a nevető gyerek - the laughing child)
Just to clarify: your dictionary is not wrong. Dolgozó means both "working" and "working person = worker". Hungarian makes little difference between adjectives (and participles) and the respective nouns. So you have magas meaning tall, and "egy magas" can refer to a tall person (or object), where you would say in English "a tall one". Likewise, "a nevető" can simply mean "the laughing person".
It is similar in Finnish, but based on your explanation I have a feeling it happens less than in Hungarian. Just a hunch, maybe I'll remember to come back here one day to comment when I know more.
Also it seems like most rooms have the same suffix, I suppose this is not a coincidence? So are they something like sleeping room, washing room etc.? (I have no idea what the first parts of the words mean, so these are just guesses).
Szoba is not a suffix, it's an own noun, simply meaning "room". Words like dolgozószoba are compound nouns. Just two nouns smooshed together, like the English "teacup" (teáscsésze, by the way. Bit of a tonguetwister. Which is also a compound noun.) So you can translate dolgozószoba as "working room", neat and simple.
Dolgozó means "working", as we already found out. Then you have fürdőszoba - bathroom. Fürdő simply means "bathing", from the verb fürdik - to bathe. Hálószoba - bedroom is a bit of a special case. The translations you can find for háló tell you it's "net" or "web", but it is also a (more archaic) word for "sleeping".
I think these three are the only ones discussed in this course that have szoba in their name. You can also have things like gyerekszoba - children's room, or várószoba - waiting room.
The living room - nappali, is also sometimes just referred to as szoba. "Gyerünk a szobába." - "Let's go to the (living) room."
I didn't mean szoba, but the -ó/-ő suffix before it. But you did answer my question with your examples, so thanks again :)
Thank you for this nice explanation, which I would like to expand a bit. Most important, "nappali" is not synonymous to "szoba". In fact, children's room or bedroom can be also referred to as "szoba". "Dolgozószoba" is not a compound of two nouns, but of a present participle (called "folyamatos melléknévi igenév" in Hungarian) and of a noun. "Hálószoba" has nothing to do with "háló" as "net" or "web". Its "háló" part is also a present participle, derived from the verb "hál", which means (if used with locative) "to sleep somewhere overnight" or (if used together with a nominal that has the suffix -val/-vel) "to have sex (with somebody)".