College Algebra & Trigonometry, 2018a

494 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
0.71 =cosB
44.7 ◦ ≈ B
Once we know the measure of ∠B, we’ll use this to find the measure of ∠C, which
corresponds to side c, the smallest side. Then we’ll subtract to find the biggest
angle.
sin 44.7 ◦
15
= sin C
9
9∗ 0.7034
15
=sinC
0.42204 ≈ sin C
25.0 ◦ ≈ C
So, with ∠B ≈ 44.7 ◦ and ∠C ≈ 25.0 ◦ , then:
∠A ≈ 180 ◦ − (44.7 ◦ +25.0 ◦ ) ≈ 180 ◦ − 69.7 ◦ ≈ 110.3 ◦
So the angles and sides of the triangle would be:
∠A = 110.3 ◦ a ≈ 53.3
∠B ≈ 44.7 ◦ b =35
∠C ≈ 25.0 ◦ c =30
If we had used the Law of Sines to find ∠A, the calculator would have returned
the value of the reference angle for ∠A, rather than the angle that is actually in
the triangle described in the problem!