Triangle formulae University of Sheffield（三角形公式谢菲尔德大学）.pdf

Triangle formulae A common mathematical problem is to find the angles or lengths of the sides of a triangle when some, but not all of these quantities are known. It is also useful to be able to calculate the area of a triangle from some of this information. In this unit we will illustrate several formulae for doing this. In order to master the techniques explained here it is vital that you undertake the practice exercises provided. After reading this text, and/or viewing the video tutorial on this topic, you should be able to • solve triangles using the cosine formulae • solve triangles using the sine formulae • find areas of triangles Contents 1. Introduction 2 2. The cosine formulae 3 3. The sine formulae 5 4. Some examples of the use of the cosine and sine formulae 6 5. The area of a triangle 9 6. Summary 12 c 1 mathcentre June 11, 2004 1. Introduction Consider a triangle such as that shown in Figure 1. A c b B a C Figure 1. A triangle with six pieces of information :angles at A, B, and C; sides a, b and c. There