College Algebra & Trigonometry, 2018a

482 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
If we go back to the diagrams we looked at earlier in this section, we can see how
this would happen:
52
40 40
38 ◦ 126.8 ◦ 53.2 ◦
C
52
40
38 ◦ 126.8 ◦
c
52
C
40
38 ◦ 53.2 ◦
c
In the first possibility ∠C would be ≈ 15.2 ◦ .
In the second possibility ∠C would be ≈ 88.8 ◦ .
52 15.2 ◦
52 88.8 ◦
40
40
38 ◦ 126.8 ◦ 38 ◦ 53.2 ◦
c
c
To find the two possible lengths for side c, we’ll need to solve two Law of Sines
calculations, one with ∠C ≈ 15.2 ◦ and one with the ∠C ≈ 88.8 ◦ .
40
sin 38
=
c
◦ sin 15.2 ◦
40
0.6157 ≈ c
0.2622
0.2622∗ 40
0.6157 ≈ c
17.0 ≈ c