TASK DEFINITION: You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For simplicity, answers should be in all lower cased letters.
PROBLEM: Category: 1930s FILMS 
Clue: In this classic film, one of the characters tries to quote the Pythagorean theorem but gets it wrong

SOLUTION: the wizard of oz

PROBLEM: Category: LEGENDS 
Clue: She abducted Lancelot when he was a baby & kept him on an island

SOLUTION: the lady of the lake

PROBLEM: Category: STATE CAPITALS 
Clue: 1 of the 2 U.S. state capitals that begin with the names of months

SOLUTION:
juneau, alaska or augusta, maine