College Algebra & Trigonometry, 2018a

11.2. THE LAW OF SINES: THE AMBIGUOUS CASE 483
With ∠C ≈ 88.8 ◦ :
40
sin 38
=
c
◦ sin 88.8 ◦
40
0.6157 ≈ c
0.9998
0.9998∗ 40
0.6157 ≈ c
65.0 ≈ c
So, our two possible solutions would be:
∠A =38 ◦ a =40
∠B ≈ 126.8 ◦ b =52
∠C ≈ 15.2 ◦ c ≈ 17.0
OR
∠A =38 ◦ a =40
∠B ≈ 53.2 ◦ b =52
∠C ≈ 88.8 ◦ c ≈ 65.0
Example 3
Solve the triangle if: ∠B =73 ◦ , b =51, a =92
Round the angles and side lengths to the nearest 10 th .
Using the Law of Sines, we can say that:
sin 73 ◦
51
= sin A
92