College Algebra & Trigonometry, 2018a

502 CHAPTER 11. THE LAW OF SINES THE LAW OF COSINES
P
b =72
C
c =?
85 ◦ p = 103
B
Now we’re working with a triangle like the one pictured above, so we can use
the Law of Cosines to find the air distance from Portland to Bend:
c 2 = b 2 + p 2 − 2bp cos C
c 2 =72 2 + 103 2 − 2 ∗ 72 ∗ 103 ∗ cos 85 ◦
c 2 ≈ 5184 + 10, 609 − 14, 832 ∗ (0.087156)
c 2 ≈ 15, 793 − 1292.7
c 2 ≈ 14, 500.3
c ≈ 120.4 miles
To find ∠P , we’ll use the Law of Sines:
sin 85 ◦
120.4 =sin P
103
sin 85◦
103∗
120.4 =sinP
103∗ 0.9962
120.4 ≈ sin P
0.85223 ≈ sin P
58.4 ◦ ≈ P