It is a long trip. (never "an"), if there´s an answer in that way, it was a typo.
That happens because of the sound.
With a "uâne" sound you use "a", example: In addition to several peacocks, she owned mallards, pheasants, bantams, and a one-eyed swan.
So, when you say "um(a)" before "olho(s), it´s "a" not "an".
The same goes to the "iu" sound, so if you have "um/uma" before a word with the "iu" sound, it takes "a". Example: university (iunivérsíri) union (iunion).
Indeed, phonetically they refer to this sound as "ju" (the j having that i-sound).
Let´s, from now on, say that in such case the letter U works as a consonant. Hence it taking the indefinite "a" before it.
Some grammarians call this "a glide", the glide in "university" makes the "u" a consonant.
"His cars is an used car" - Let me correct this one.
It would be either "his car is a used car." or "his cars are used cars".
Notice that there´s the "iu" (ju) sound here, so the article is "a" before the word "used".
Notice also that the plural of "a used car" is "used cars" (the article "a" is dropped when it turns into its plural form).
Guys and also why a European and an FBI agent is correct please.
That is correct. It´s right, because before an vowel you have "an".
I know I know, you are going to ask "where is the vovel there?", let´s back to the vowel sound. F, the "e" is there when we pronounce it, éfe, see? It´s not always that it happens, but from now on every time you have "FBI" in a sentence you will know that before that it´s A rather than "AN".
I hope this helps.