Pre-Calculus All-in-One For Dummies

Chapter 14

Getting the Slant on Oblique Triangles

IN THIS CHAPTER

Mastering and using the Law of Sines

Wielding the Law of Cosines

Utilizing two methods to find the area of triangles

In order to solve a triangle, you need to find the measures of all three angles and the lengths of all three sides. You’re given as many as three of these pieces of information and you need to find the rest. So far, in this book, you’ve seen mainly right triangles. In Chapter 8, you find the lengths of missing sides of a right triangle using the Pythagorean Theorem, find missing angles using right-triangle trigonometry, and evaluate trig functions for specific angles. But what happens if you need to solve a triangle that isn’t a right triangle?

You can connect any three points in a plane to form a triangle. Then comes the fun of determining all the measures of that triangle. Finding missing angles and sides of oblique triangles (acute or obtuse triangles) can be more challenging because they don’t have a right angle. And without a right angle, the triangle has no hypotenuse, which means the Pythagorean Theorem is useless. But don’t worry; this chapter shows you the way. The Law of Sines and the Law ...