TABLE OF CONTENTS Triangles are perhaps the most important of geometric figures in engineering and technology and appropriately receive considerable attention. Triangles are often seen in structures in the form of trusses and guy wires. Mechanical forces acting along the lines of these structures are resolved into component forces using laws of trigonometry. This process is called triangulation. Surveyors use triangulation to measure elevations and distances. In fact, the Greek mathematician Eratosthenes (circa 276 196 BC) estimated the circumference of the earth with extraordinary accuracy using a large triangle based on the simultaneous measurement of the angles between the sun and the Egyptian cities of Syene and Alexandria. In electrical engineering, triangles are used for calculations involving alternating current and three-phase power.
The list of applications for triangles is very long. In this chapter, the fundamental rules of triangles are presented and the foundation laid for the study of trigonometry. The essential laws of trigonometry are presented in Chapter 20.
To aid in the solution of problems involving triangles, certain auxiliary lines or constructions are sometimes drawn. These lines and constructions include the angle bisector, circumscribed circle, inscribed circle, and altitude.
All of the special lines and constructions discussed in this section can be determined using only a straight edge and compass. These are called geometric con structions and are not discussed in this book. If interested, consult a good drafting book to learn how these constructions are done.
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