"You are happy."
You wouldn't say 我高兴？It's a set phrase with 很。(Cred: Mr.Elia)
Since 是 is not used with adjectives, 很 is used in replacement.
"Tips and notes
When we want to describe something we don’t use the verb “to be”, we have to put something else before an adjective. The most common word used to do this is 很 hěn, which literally means very. It goes between the subject (who or what we are describing) and the adjective (what we are describing it as). Since 很 is used so often like this, it oftentimes doesn’t mean “very”, just a link between a noun and an adjective."
I remember my Chinese teacher explaining to me once that Chinese sounds very awkward with an odd number of syllables in a sentence or phrase, so sometimes another word is added in to even it out even if it's not really needed for clarity. So in this case, 'hen' seems unnecessary to us but the sentence sounds awkward without it.
Because it's a question and not a statement(describing something) is what im thinking. Just like you don't say "ni hen hao ma?" You say ni hao ma? (You good?, how are you?) So im guessing saying someone is good should logically be, "ni hen hao".
The statement "you are happy" is "ni hen gao xing", for that reason. The question form is "ni gao xing ma", and not "ni hen gao xing ma". In that case, you might be asking: "are you very happy?". I'm not a pro at Mandarin so just double check to be sure.
很 is used when the adjective is without any adverb? Sorry the source is Japanese but I put it :http://calend-okinawa.com/culture2/chinese/henzhongwen.html
This exactly. Since the accepted answer for the 我 statement was 我高興 (I use traditional, since that's what I'm more familiar with), there should be a much clearer explanation as to why 你很高興 is the correct answer and 你高興 isn't. (I know that I've often heard 很 used in the manner explained in an earlier post, in front of adjectives. But the lack of a grammar explanation makes it frustrating when one slightly different option is accepted while the other isn't.)
I am a native speaker of Chinese and I was confused of the "very" in the translation. I realized that whenever I am stating that someone is happy, I would say in translation of English, you are very happy. Saying "you are happy" in Chinese sounds like a question of "Are you happy?"