http://www.ck12.org Chapter 8. Right Triangle Trigonometry
Solution:Use the second equation to solve for^6 B.
b^2 = 262 + 182 − 2 ( 26 )( 18 )cos 26◦
b^2 = 1000 −936 cos 26◦
b^2 = 158. 7288
b≈ 12. 60To findm^6 Aorm^6 C, you can use either the Law of Sines or Law of Cosines. Let’s use the Law of Sines.
sin 26◦
12. 60=
sinA
18
12. 60 ·sinA= 18 ·sin 26◦sinA=18 ·sin 26◦
12. 60sin−^1
( 18 ·sin 26◦
12. 60)
≈ 38. 77 ◦To findm^6 C, use the Triangle Sum Theorem.26 ◦+ 38. 77 ◦+m^6 C= 180 ◦
m^6 C= 115. 23 ◦Unlike the previous sections in this chapter, with the Laws of Sines and Cosines, we have been using values that we
have found to find other values. With these two laws, you have to use values that are not given. Just keep in mind
to always wait until the very last step to put anything into your calculator. This will ensure that you have the most
accurate answer.
Example 4:Solve the triangle. Round your answers to the nearest hundredth.
Solution:When you are given only the sides, you have to use the Law of Cosines to find one angle and then you
can use the Law of Sines to find another.