People who wanted to apply complex Algebra to real world concepts, like equations of a slope on a bridge founded analytic geometry.
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Artem Analyticam
In geometry, angles are studied mostly in relation to each other. In Trigonometry, angles are studied in relation to side lengths and triangles.
It allowed points in space to be described algebraically. This allowed lines and curves to be described using algebra. Bringing together algebra and geometry meant that tools that mathematicians had developed for solving algebraic problems could be applied to problems in geometry and tools from geometry could be applied to algebra.
The Tangemt Formula for Geometry is opposite over adjacent, or opp./adj.
In Geometry, you learn about triangles. In Trigonometry you learn even more about triangles.