College Algebra & Trigonometry, 2018a

474 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
In this problem we’re given two angles and one side. It’s important that the side
we’re given corresponds to one of the known angles, otherwise we wouldn’t be
able to use the Law of Sines.
a
b
45 ◦ 95 ◦ 5
A
Since we know two of the angles, then the third will just be 180 ◦ − (45 ◦ +95 ◦ )=
180 ◦ − 140 ◦ =40 ◦ = ∠A. To find the lengths of the unknown sides, we’ll use the
Law of Sines. We should start by choosing a side-angle pair for which we know
both the side and the angle. In this case, we know that ∠C =95 ◦ and side c =5.
c
sin C = b
sin B
5
sin 95
=
b
◦ sin 45 ◦
If we multiply on both sides by sin 45 ◦ , then
sin 45 ◦ 5
∗
sin 95
= b ◦
To arrive at an approximate value for sin 45 ◦ 5
∗
sin 95
, we can say:
◦
5
0.7071∗
0.9962 ≈ b
3.55 ≈ b
To find the length of side a, I would recommend that we use the exact side-angle
pair that was given in the problem, rather than using the approximate value of
side b that we just solved for.