http://www.ck12.org Chapter 8. Right Triangle Trigonometry
8.7 Extension: Laws of Sines and Cosines
Learning Objectives
- Identify and use the Law of Sines and Cosines.
In this chapter, we have only applied the trigonometric ratios to right triangles. However, you can extend what we
know about these ratios and derive the Law of Sines and the Law of Cosines. Both of these laws can be used with
any type of triangle to find any angle or side within it. That means we can find the sine, cosine and tangent of angle
that are greater than 90◦, such as the obtuse angle in an obtuse triangle.
Law of Sines
Law of Sines:If 4 ABChas sides of length,a,b, andc, thensinaA=sinbB=sincC.
Looking at a triangle, the lengthsa,b, andcare opposite the angles of the same letter. Let’s use the Law of Sines on
a couple of examples.
We will save the proof for a later course.
Example 1:Solve the triangle using the Law of Sines. Round decimal answers to the nearest tenth.
Solution:First, to findm^6 A, we can use the Triangle Sum Theorem.
m^6 A+ 85 ◦+ 38 ◦= 180 ◦
m^6 A= 57 ◦