Learn Croatian: On radi oštrim alatom. - He works with a sharp tool.

In Croatian, when you use a physical object as an instrument to do something (like working with a tool or writing with a pen), you use the instrumental case entirely on its own. You only use the prepositions s or sa when talking about company, like going somewhere with a person.

How do we form the adjective oštrim to match alatom?

Alat (tool) is a masculine noun, and in the instrumental case, it takes the noun ending -om to become alatom. To make an adjective agree with a masculine (or neuter) noun in the instrumental case, we add the adjective ending -im. This is why we use oštrim.

If the dictionary word for "sharp" is oštar, why is there no "a" in oštrim?

This happens because of a common spelling rule often called the "fleeting a". In many Croatian adjectives and nouns ending in a consonant plus -ar or -ac, the a disappears when you add a grammatical ending. The base oštar drops its a to become the stem oštr-, and then we add the -im ending.