Questions & Answers about رأينا أفعى تحت الشجرة.
Why does رأينا have a ي in the middle when the base verb is رأى?
رأى (he saw) is a "defective" verb, meaning its root ends in a weak letter (an alif maqṣūra here). When you add a past-tense subject suffix that starts with a consonant, like the "we" suffix ـنا (-na), that weak ending turns into a ي (ya) with a sukun pause. So it becomes رأيْنا (ra'ay-na).
Since أفعى is the object of the sentence ("a snake"), why doesn't it have an "an" (tanween fatha) ending?
أفعى ends with an alif maqṣūra (ى), which produces a long "a" sound. Arabic doesn't add visible vowel markers (like the accusative tanween fatha) on top of this letter because it would be too hard to pronounce. The word is grammatically in the accusative case as the object, but its case ending remains hidden.
Why does the word for "under", تحت, end with an "a" vowel (fatha)?
In Arabic, words that specify a location or time (like تحت for "under" or فوق for "above") act as adverbs of place. These spatial adverbs are generally put in the accusative case by default, which is why تحت ends with a fatha.
What grammatical case should الشجرة (the tree) be in?
It takes the genitive case, so it ends with a kasra (الشجرةِ). Any noun that directly follows a spatial adverb like تحت acts as the second half of a possessive phrase (an idaafa construction), which forces that noun into the genitive case.