Final answer:
Max Weber is the German social scientist who identified three sources of legitimacy, which are traditional, charismatic, and legal-rational authority.
Step-by-step explanation:
The 20th century German social scientist who identified three sources of legitimacy was Max Weber. Weber's work on the nature of authority and legitimacy is fundamental to sociology and political science. His model distinguishes three types of legitimate authority: traditional, charismatic, and legal-rational, each of which corresponds to how individuals or institutions project and maintain social power. Weber also examined other sociological and economic aspects, including the relationship between religions, specifically Protestant ethics, and the development of capitalism. Weber's multidimensional analysis of society remains influential in understanding complex social dynamics and institutions.