Pre-Calculus Workbook For Dummies, 3rd Edition

Chapter 10

Solving Oblique Triangles

IN THIS CHAPTER

Using the Law of Sines and the Law of Cosines to solve triangles

Solving word problems using oblique triangles

Finding the area of a triangle

The trigonometry functions sine, cosine, and tangent are great for finding missing sides and angles inside right triangles. But what happens when a triangle isn’t quite right? This type of triangle is known as an oblique triangle — any kind of triangle that isn’t a right triangle. As you see in Chapter 6, the process of finding all the sides and angles in a triangle is known as solving the triangle. This chapter helps you figure out that process for oblique triangles.

As long as you know one angle and the side directly across from it (plus one more piece of information), you can use the Law of Sines to solve the triangle. The Law of Sines can be used in three different cases: angle-side-angle (ASA), angle-angle-side (AAS), and side-side-angle (SSA). The first two cases have exactly one solution. The third case is known as the ambiguous case because it may have one, two, or no solutions. You’ll see an explanation of each case to show you how to deal with them. In fact, the ambiguous case ...