Explore rational trigonometry from first principles in this 33-minute video lecture. Learn about quadrance and spread as algebraic replacements for distance and angle, using a vector approach. Discover the importance of the scalar/inner/dot product in introducing perpendicularity and spread between vectors. Master the five main laws of rational trigonometry: Pythagoras' theorem, Triple quad formula, Cross law, Spread law, and Triple spread formula. Engage with exercises to prove these laws, with helpful hints provided. Gain insights into this purely algebraic approach to trigonometry and geometry at an elementary level.