Why an adjective afte a verb ?
because /to appear/ is in the semntic category of /to be/, which usually requires
adjectives as (in one of its several usages) it joins a noun to a state for it, i.e. an adjective.
Or, just examine to the longer expression:
The problem appears to be impossible to solve.
I think you will not have any doubt that in THIS expression
you need the adjective.