I take it you mean ça, since ca isn't a word in French. In that case, no, because ça is a pronoun, not an adjective; you won't find it modifiying a noun like that. As DianaM mentioned, the adjective for "this/that letter" would be cette, and that would be hard to mistake for sa.
Duolingo doesn't always show the conjugation table; it seems to be a bug. I just use this site:
I think Wordreference is a superior site for French conjugations.
That's one way I took it. I also thought of it as him expanding on the letter. Maybe he turned it in to his teacher as a first draft, and now he's going back to make sure all sentences are complete, each idea he wants to express is fully laid out, etc. Or maybe there's some artistic flair in his letter, and he finally figured out how to complete his creative concept. There are numerous ways to improve any written document.
Just a little correction, if you don't mind. "Sa" is actually a possessive adjective, not an article. It serves here also as a grammatical "determiner", so no article is required, since we always have only one determiner for each particular noun.
"Le garçon améliore sa lettre." That is, precisely the same as "the boy is improving his letter". As has already been pointed out, the gender of the possessive ("son" or "sa") conforms to the gender of the object owned, and has nothing to do with the gender of the owner. Since "lettre" is a feminine noun, the possessive must be "sa".
In simple sentences, you can assume that the possessive relates to the subject.
If it were "her" letter, the French sentence would need to point to the fact that it is not "his", since the possessive is the same:
the boy is improving her letter = le garçon améliore sa lettre à elle
I intentionally chose to respond with "her letter" to see if Duo would accept it. It did not. So are you saying that in French, you would always take the time to specify the gender if there was any chance of confusion? In other words, if I knew my brother had edited my sister's letter and I was relating this to a friend, I would not say "sa lettre" with the expectation that my friend would understand from context?
That would be completely misunderstood as a translation of the French.
"A letter" in English and "une lettre" in French can be either a written communication or a graphic symbol. In English, in the latter case, a "letter" refers to a symbol from our own alphabet, while a "character" refers to a different sort of symbol - a Chinese character, for example. As I understand it, the French use "lettre" to refer to both kinds of symbols.
So, while it is technically possible that "Le garçon améliore sa lettre." could refer to the boy improving his rendition of some Chinese character, there is just no way that "The boy improves his character" would convey that meaning to any English speaker. To "improve one's character" would invariably be taken to mean doing something to make oneself a better person - and that is not what the French sentence says..
There is a reason that "letter" is listed as the top-most hint. Other hints may be possible depending on the context, but by venturing into that territory, you may unintentionally change the meaning. It is always preferable to go with the most likely meaning. DL is not designed to reward more creative "translations".
"Ameliorate" is a very formal version of "improve". "Améliorer", as I understand it, is much less formal; it's just the word for "improve" in French. Matching the level of formality is one of the important aspects of translation, therefore "improve" is the better translation.
That said, the main reason "ameliorate" was not accepted is probably because no one thought to include it in the list of acceptable responses. In general, I find DL is pretty (overly?) accommodating about differences in register.
Grammatically, both "son" and "sa" may be either "his" or "her". The French possessive adjective must match the gender and number of the noun it modifies. I.e.,
- sa lettre (f) = his letter (or) her letter
- son livre (m) = his book (or) her book
In a sentence like "Le garçon améliore sa lettre", it would be understood as "his letter" because of the subject of the sentence, "le garçon". If you wanted to say "the boy is improving her letter", you would say "Le garçon améliore sa lettre à elle".
If DL actually refused to accept "her" for "son", that would be DL's mistake and should be reported. I admit, however, that since there is no place in the sentence we were given to put the word "son" in translation, I'm thinking that you might have made an error of your own. "Lettre" is a feminine noun and must be "sa", whether the meaning is "his" or "her". It cannot be "son lettre".
DL sometimes gives peculiar "reasons" for marking something wrong - that is, the translation can be wrong, but DL will indicate a different word than the actual mistake. No wonder you're confused!
Conventionally, the object belongs to the subject.
In 3rd person singular, the possessives are identical for "il" and "elle", because they agree with the possession and they do not give any indication of the owner's gender.
The boy improves his letter = Le garçon améliore sa lettre
The boy improves her letter = Le garçon améliore sa lettre à elle.
The best translation is the one which conveys the meaning of the original sentence naturally in the target language. If you feel compelled to translate "améliorer" as "to ameliorate", you have chosen the sound-alike version over the natural version. So you have to ask yourself, do you really use the English word "ameliorate" in conversation when you want to say that you are improving something or making it better.
"sa" can translate to "his / her / its".
"sa" is an adjective, and as such it has to agree in gender and number with the noun it modifies:
- sa lettre (feminine singular) = his/her/its letter
- son livre (masculine singular) = his/her/its book
- ses lettres et ses livres (plural) = his/her/its letters and his/her/its books
In other words, "son, sa, ses" does not give you the gender of the owner.
French possessives are adjectives. As any other adjectives, they agree in gender and number with the noun they modify.
- sa lettre (feminine) = his/her/its letter
- son livre (masculine) = his/her/its book
- ses lettres (feminine plural) = his/her/its letters
- ses livres (masculine plural) = his/her/its books