ABSTRACT
Spherical trigonometry is the key to the study of the precise relationship among distances and angles on the sphere. Central to this is the relationship among the distances and angles in a triangle. The central geometric difference between the plane and the sphere is, of course, the fact that the sphere is curved. This chapter discusses the properties of right triangles on the sphere by using the spherical Pythagorean theorem and the Geber’s theorem. It derives several formulas which express trigonometric relationships among the sides and angles of a spherical triangle. These will all be consequences of the spherical laws of sines and cosines and the analogue formula derived from the law of cosines. The chapter also discusses how to find the measures of the sides and angles of a spherical triangle.
