Learn Finnish: Lentoemäntä tietää matkustamon olevan hiljainen. - The flight attendant knows that the cabin is quiet.

This is the referative construction, which is a shorter way to replace an että (that) clause. Instead of saying Lentoemäntä tietää, että matkustamo on hiljainen, we use the present active participle of olla (olevan) and drop the word että.

Why is the word for cabin, matkustamo, in the genitive case (matkustamon)?

In this construction, the subject of the original että clause always takes the genitive case. Since "the cabin" is the subject of the "being quiet" part, matkustamo becomes matkustamon.

If the subject is matkustamon, why does hiljainen (quiet) stay in the nominative instead of matching the genitive?

When the participle is olevan (from olla, to be), the describing adjective stays in the exact same case it would have in a normal sentence. Because a normal sentence is matkustamo on hiljainen (nominative), the adjective hiljainen doesn't change to match the genitive subject.

Does the main verb tietää trigger this specific construction?

Yes! This structure is specifically used after verbs of expressing, thinking, or perceiving. Common verbs that trigger it include tietää (to know), nähdä (to see), kuulla (to hear), and sanoa (to say).