Question

In which sentence does the adverb clause modify an adjective?

Answer 1

The sentence in which the adverb clause modifies an adjective is the second one - The veteran appeared proud as he saluted the flag.
The adjective here is proud, and the adverbial clause is as he saluted the flag. As you can see here, that clause is describing the adjective in more detail. 
When did the veteran appear proud? - As he saluted the flag (it obviously modifies the word proud)