"Plane trigonometry" is a branch of mathematics that focuses on the relationship between the sides and angles of a triangle. Plane trigonometry builds upon the basic concepts of Euclidean geometry, and it has applications in a variety of mathematical fields, from physics to advanced calculus.
Celestial navigator Eric DeMan explains that plane trigonometry examines the vertices of a triangle and the surfaces of the planes that cover its three unique sides. Since triangles are composed of straight lines, understanding the relationship between the angles that make up a triangle is essential to understanding plane trigonometry.
The Encyclopaedia Britannica further defines plane trigonometry as an attempt to deduce the remaining sides of a triangle from the sides that are known. While this may seem like the definition of trigonometry, plane trigonometry takes the concept to a higher level of understanding. Traditional geometry only explains the nature of triangles that follow the basic rules of the Euclidean plane. Plane trigonometry goes beyond the Euclidean plane, explaining the nature of more complex relationships between triangles. Plane trigonometry works entirely through logic and deduction, inferring one set of facts about a given triangle based on what is known about the triangle's other angles, vertices and planes.