Hi, it is a mistake to say Hello = Dobrý den. Hello means Ahoj / Hallo, and it is informal (can be said to a friend and otherwise shouldn't be used). Dobrý den = Good day / Guten Tag, and it is formal (it is almost a non-sense to say it to a friend). This leads to a misuse. Secondly, in Czech Republic it is actually unpolite to not distinguish formal and informal. So if you mix it, it will be either a) unpolite or b) non-sense. Hope that helps.
Hello is used in quite formal context today as well, we do not live in Victorian England. It is much closer to Dobrý den and Guten Tag.
Ahoj is closer to Hi. It would be highly misleading to suggest that you can say Ahoj, where you say Hello in English. Hello can be used in more formal occasions than Czech Ahoj.
Hmm, you are right, Hello is used quite formally. Also Hallo is quite formal. And Hi is a good translation of Ahoj.
The problem is Dobrý den can't be used informally - or would you say Hello is used only formally? I have found on the internet that Hello is informal. That is why i think it's misleading. The accurate translation of Dobrý den would be Good day. It is formal, it shows what the individual words mean... but it's dated so it seems this doesn't have a perfect solution.
My comment is not about translations but about usage.
On the English side... I would rank the most common greetings, at least in the US (East Coast/Mid-Atlantic region), from "really informal and could be considered really rude" to "really formal and almost never used" as: Yo - Hey - Hi - Hello - Good day. I'd suggest "Hello" as the best all-around option, for anyone who's not sure whether one of the others would suit a particular situation. On the Czech side, it seems to me that you can't go wrong with Dobrý den as a general greeting, at least for most of the day.
My opinion of US use: 1. In the morning, with everyone - (formal meetings, friends, family, co-workers) = Good morning is fine and appropriate, but usually only when greeting someone or a group. So equating this to Dobre rano seems appropriate to US English
In the morning, when departing from anyone (friends, family, formal), it's usually not common to say just "Good morning", but "Have a good day" or "Have a good morning".
In the afternoon, when arriving and meeting anyone (formal or informal), it is common and appropriate to say "Hello" and much less common to say "Good afternoon", although if you're addressing a group, something like, "Good afternoon, everyone" is appropriate. When addressing a group in the afternoon, you would usually say "Good afternoon, everyone" or "Hello Everyone". When departing, its the same as #2
In the evening, it's the same as #3 except you insert "...evening..." instead of "...afternoon...", but "Ahoj" seems appropriate to US English in formal and informal circumstances
When departing in the evening: formal or informal - "Have a good evening" is perfectly acceptable and more common than "Good evening" by itself. "Have a good night" or "Good night" is also perfectly formal or informal
With all, "Good night" would be more appropriate than "Have a good night" or "Good Evening"; a simple "Dobrou noc" seems appropriate to a US English speaker
It's subtle and you can say it, but in US English, it would be a bit overly formal (and with an exclamation point or overemphasis spoken tone, would definitely take that "dismissing" tone you mention (the word, "dismissing" in US English, is usually a negative connotation).
If I were learning English, I wouldn't want my teacher spending too much time on this issue, because the way you're saying it is just fine, but my wife, who is Czech, is always telling me about the Czech subtleties, because she hears me practicing out loud and she'll tell me, "Czechs really won't say it that way."
So to emphasize, if I was leaving someone's company in the morning or afternoon, I would say "Have a good morning (afternoon)" or "Have a good day"
I mistakenly wrote "Good morning, thank you!", but got it correct. "Good morning" I know to be "Dobrý rano", so should I have been marked wrong in this case? Also, would "Good day" be an acceptable equivalent to "Hello" for "Dobrý den"?
I'd post the screenshot, but the option isn't available here.
There is "formal" and there is "polite". They may coincide and may be very different. I suggest distinguishing them carefully here. You can be polite to your closest intimate friend and you can be formal when speaking with a person you despise. Those situations call for very different language choices.
There are etiquette rules when to use "Dobrý den" and a sentence in Duolingo can't teach you those rules.
We consider "Hello!" to be the best possible and the most universal translation of "Dobrý den!".