is fine an adjective
fine adjective or adverb. It's an adjective functioning as a Predicative Complement. A Predicative Complement is a Complement of the verb that describes the Subject or Object. In this case it is describing the Subject. Predicative Complements can be noun phrases, adjective phrases and preposition phrases, but hardy ever - if ever at all - adverbs. The reason we use an adjective phrase here is that this phrase is describing a noun phrase. Modifiers of noun phrases are usually adjectives, not adverbs. Consider the following examples: I'm happy. I'm cold. I'm assiduous. *I'm happily. (adverb as PC, ungrammatical) *I'm coldly.