Dear Miss Snark,
If I have completed writing a nonfiction book, do I still need to have a book proposal? Could I find an agent for it instead using the same materials as with a work of fiction as it is done? I.e. a one page query letter and a one page synopsis with sample chapters or the completed work available upon request.
Yes, you can do that for the query, but you will need a proposal for the next step. Non fiction editors read proposals, not finished books, to decide if they will acquire (generally). Unless you're querying memoir, you gotta have a proposal. Memoir is sold like fiction (sample chapters, and frequently finished if you're a new writer).
The critical piece in a proposal is 1. who will read this book; 2. what new do you have to contribute to the discussion; 3. why you are the person to write this; and 4. What other books are currently on the market that address this topic. You don't need any of that in fiction, but you'll need it even if your book is finished for non fiction.