In recent decades, many people have come to believe that an imaginary area called the “Bermuda Triangle,” located off the southeastern Atlantic coast of the United States, has been the site of a high incidence of losses of ships, small boats, and aircraft over the centuries. The U.S. Board of Geographic Names does not recognize the “Bermuda Triangle” as an official name and does not maintain an official file on the area.
Assume for the moment, without judging the merits of the hypothesis, that the “Bermuda Triangle” either has vertices in Miami (Florida), San Juan (Puerto Rico), and Bermuda, or it has vertices in Norfolk (Virginia), Bermuda, and Santiago (Cuba). In this chapter, you will develop a formula that determines the area of a triangle from its perimeter and side lengths. Which “Bermuda Triangle” has a larger area: Miami-Bermuda-Puerto Rico or Norfolk-Bermuda-Cuba? You will calculate the answer in this chapter.*
*Section 7.3, Exercises 37 and 38.
IN THIS CHAPTER, we discuss oblique (nonright) triangles. We use the Law of Sines and the Law of Cosines to solve oblique triangles. Then on the basis of the Law of Sines and the Law of Cosines and with trigonometric identities, ...