Learn Arabic (Modern Standard): هذا الشاي حار جدا.

The word جدا (jiddan) acts as an adverb here. In Arabic, adverbs usually take the accusative case. For indefinite words, this case is marked by an "an" sound at the end. When written, this ending usually requires adding a visible Alif to the end of the word, which is exactly the rule you are learning in this lesson!

Where is the word for "is" in this sentence?

Arabic does not use a word for "is" or "are" in the present tense. The sentence literally reads "This the-tea hot very." When you put a subject (هذا الشاي) and a descriptive word (حار) side by side, it automatically creates an "is" sentence.

Why does الشاي (tea) have the word "the" attached to it if the translation just says "this tea"?

In Arabic, to say "this specific thing", you must put "the" (ال) on the noun. So, هذا الشاي literally means "this the-tea", which translates as "this tea". If you left off "the" and just wrote هذا شاي, the meaning would change to "This is a tea."

Why don't we hear the "L" sound in the word الشاي (ash-shāy)?

The word الشاي starts with a "sun letter" (the letter sheen, ش). When you attach "the" (ال) to a word starting with a sun letter, the "L" sound is swallowed by the first letter of the word. Instead of saying "al-shāy", you merge the sounds and say "ash-shāy".