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Why is the sum of the angles of spherical triangles always larger than the sum of the angles of plane triangles?
Because, to allow for the curvature of the spherical surface, each angle must be slightly larger than its plane-surface equivalent.
What is the difference between plane trigonometry and spherical trigonometry?
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
What is the difference of plane and spherical triangles?
The main difference is that the plane triangle is on a flat surface while the spherical triangle is on the surface of a sphere. One consequence is that the angles of a plane triangle sum to 2*pi radians (180 degrees) while those on a sphere sum to more than 2*pi radians.
What are the two branches of Trigonometry?
The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.
What is the importance of trigonometry in navigation?
Navigation takes place on the surface of a sphere, and it involves angles and distances. Spherical trigonometry was developed from plane trigonometry so that navigators could find their away over the Earth's surface.
