That would imply that "unhappy" is an adverb (and should probably be unhappily if you want to split hairs). I'm not 100% sure but I think it would be "misere" in Latin.
The difference being that one describes the noun (adjective) and the other describes the action (adverb)
You bring up an excellent point, but in English, we are a bit limited on how we use our words due to the nature of the language. Latin flows much more freely. Unhappy, the student goes to school, the student goes to school unhappy, the unhappy student goes to school are all ways to say the same thing. I'll while using the adjective for of miser. Basically Latin can have mini subordinate clauses. "The student, being unhappy, goes to school." Later on you'll see adjectives in the ablative being used adverbially.
There is a difference between "The student goes unhappy(LY) to school," and "the unhappy student goes to school." In the first sentence the fact that he goes to school gives an unhappy feeling, in the second form the student may be unhappy AND goes to school (which even could make him happy because he is now away from home).
Probably because that sentence uses 'unhappy' adverbially.
'The student goes to school (while being) unhappy' or 'The student goes to school unhapp(il)y'.
If it were an adjective, it would be attached to its noun, but this degree of separation, while it can technically be accepted, especially in a more poetic word order, only makes sense as an adverb.