Sentence Diagramming: The bird in the tree sang happily
The prepositional phrase here is describing the type of bird by giving its location. If the sentence were to be phrased "The bird sang happily in the tree", it would be answering the question where as you said. It would then be supporting the verb sang. However, currently, the prepositional phrase is describing the bird, and the question "Where?" is an adverbial answer, and therefore cannot describe the noun bird.