Explore the intricacies of the Cross law in Universal Hyperbolic Geometry through this comprehensive 35-minute video lecture. Delve into the fourth and most complex of the main trigonometry laws in hyperbolic settings, learning its proof through a remarkable polynomial identity. Discover the law's application to the relationship between quadrance and spread in equilateral triangles. Follow along as the lecturer reviews the Euclidean Cross law, introduces the hyperbolic version, and provides a detailed proof with computational assistance. Engage with exercises and explore the pleasant consequences of this powerful law, including the Equilateral triangle theorem. This lecture offers a deep dive into advanced geometric concepts, suitable for those with a strong foundation in mathematics and an interest in hyperbolic geometry.