Learn Icelandic: Hundurinn situr á háum kletti.

It changes because it describes the masculine noun kletti (cliff), which is in the dative case. In the strong declension, dative singular masculine adjectives take the -um ending. So, the base word hár becomes háum.

What makes kletti and háum take the dative case here?

The preposition á (on) causes this. When á is used to show a stationary location or resting place (like sitting on a cliff), the noun and adjective following it must be in the dative case. If the dog were jumping onto the cliff (movement), they would take the accusative case.

Wait, if the word is kletti, how do I know it is a masculine noun?

Kletti is just the dative form. The dictionary (nominative) form of the word is klettur, which is a regular masculine noun. Many masculine nouns that end in -ur drop the -ur and add an -i in the dative case.

Why do we use the strong adjective form háum instead of a weak form?

We use strong adjectives when the noun is indefinite, meaning there is no 'the' or other specific pointer attached to it. Since the dog is sitting on 'a' high cliff, kletti is indefinite, and the adjective takes the strong dative ending -um.