Here's why:
* Adjectives describe nouns or pronouns. In this case, "desperate" describes the situation.
* Indirect Objects receive the direct object. This sentence doesn't have an indirect object.
* Predicate Nominatives are nouns or pronouns that rename the subject. This sentence doesn't have a predicate nominative.
* Objective Complements are adjectives or nouns that follow a direct object and modify it. This sentence doesn't have an objective complement.
Therefore, "desperate" is an adjective modifying the noun "situation".