**ERIC Number:**EJ875484

**Record Type:**Journal

**Publication Date:**2005

**Pages:**6

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

Solving Triangles

Jarrrett, Joscelyn

AMATYC Review, v27 n1 p3-8 Fall 2005

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.

Descriptors: Textbooks, Geometric Concepts, College Mathematics, Two Year Colleges, Mathematics Instruction, Problem Solving, Mathematical Logic, Validity

American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A