Chapter 17
Obeying the Laws and Applying Them
IN THIS CHAPTER
Finding missing parts in triangles
Understanding the laws of sines and cosines
Computing the areas of triangles
Triangles are very useful figures. Since humankind figured out how to keep records, people have documented the applications of triangles in mathematics and many other sciences and the arts. The right triangle gets the most use; Pythagoras saw to it that others recognized right triangles for the powerful polygons that they are. But oblique triangles (those that aren’t acute triangles or right triangles) have their place, too. You can’t always arrange to have a nice right triangle when you want it. Here’s where oblique triangles and the laws of sines and cosines come into play.
The law of sines uses — believe it or not — the sines of a triangle’s angles. With three carefully selected parts of the triangle (there are six to choose from), you can solve for the sizes of all the other parts. Of course, you have to obey the law, and the choices you can make are limited. That’s where the law of cosines comes in to save the day. This law isn’t as user-friendly, but it picks up where the law of sines falls short.
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