"The tiger eats in the zoo."
Translation:La tigre mangia nello zoo.
In Latin there was a tendency to use masculine in prose but feminine in poetry for tigris, although Pliny used feminine. It's masculine in Spanish, el tigre, and also masc in German and French. Your comment about masc grammatical gender as literary Italian is interesting and not surprising given the situation with how the lexeme worked in Latin. In Modern Greek, it's feminine η τίγρης, as ancient Greek ἡ τίγρις.
To paraphrase wikibooks - "Animals and things may be masculine or feminine, but there is no clear rule for this association. When you learn a new word, you should learn whether it is masculine (il serpente) or feminine (la tigre) or either (il gatto/la gatta)." Don't just love grammar exceptions?
It's the same rule that is behind the use of il and lo: http://www.bbc.co.uk/languages/italian/language_notes/il.html
For historical reasons (that is the transition from Latin to Italian), some word endings are inconsistent.
There are a few words ending in -e in their singular form (-e is usually the marker for feminine plural words) that are masculine or feminine singular.
Masculine: fiume-fiumi, principe-principi, cane-cani, fiore-fiori...
Feminine: voce-voci, foce-foci, arte-arti, neve-nevi, tigre-tigri...