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The AMATYC Review Fall 2005, Vol.27, No.1 |
Solving Triangles Joscelyn Jarrrett |
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Joscelyn A. Jarrett is a professor of mathematics at Gordon College in Barnesville, Georgia, He received an MS in mathematics from the University of Toronto and a PhD in mathematics education from the University of Iowa. E-mail: j_jarrett@gdn.edu |
| This article discusses the four categories of triangles that are standard in most textbooks when "solving" triangles: (a) Given the lengths of two sides and the measure of an angle opposite one of the two given sides, (b) Given the lengths of two sides and the measure of the included angle, (c) Given the lengths of all three sides, d) Given the lengths of one side and the measure of two angles. It then introduces two new categories of solving triangles: (e) Given the measures of two angles and the perimeter of the triangle, and (f) Given the measures of two angles and the area of the triangle. These two new categories require the use of two non-standard theorems which are stated and proved in the article. One of the two theorems is an extension of the Law of Sines to include the perimeter. The other provides a relationship among the area, angles, and the perimeter of a triangle. Furthermore, the article gives four applications of the use of these theorems in solving problems of the two new categories introduced. | |