Learn Arabic (Modern Standard): القصة الممتعة في الكتاب الجديد. - The interesting story is in the new book.

In Arabic, an adjective must match its noun in "definiteness." Because the noun القصة (the story) is definite and starts with الـ (al-), the adjective describing it must also start with الـ. Even though it literally looks like "the story the interesting," it translates simply to "the interesting story."

Why does الممتعة end with a taa marbuuta (ة) while الجديد does not?

Adjectives must match the gender of the noun they describe. القصة (the story) is a feminine noun, which we can usually tell by its ة ending, so its adjective الممتعة (interesting) also takes the feminine ة ending. Meanwhile, الكتاب (the book) is masculine, so its adjective الجديد (new) stays in its standard masculine form.

Why do the adjectives come after the nouns in this sentence?

Unlike English, which puts the adjective first (like "new book"), Arabic places the describing adjective immediately after the noun. That is why we see الكتاب الجديد (the book the new) instead of the other way around.

There is no word for "is" in the Arabic sentence. How do we know it means "is in the new book"?

Arabic does not use a word for "is" in the present tense! This is a "nominal sentence" made of two parts: the subject القصة الممتعة (The interesting story) and the information about it في الكتاب الجديد (in the new book). The "is" is automatically understood to exist between these two halves.