Given A =°16 , b =12 , and a = 10 , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two
Decimal places.
A) c =18.62
B) c = 2.10 and 20.97
C) c =19.75
D) c =1.12 and 17.85
E) not possible

Question

Quizplus · Accepted Answer

We can use the Law of Sines to solve for c:
sin A / a = sin B / b = sin C / c
sin 16 / 10 = sin B / 12
sin B = (sin 16 / 10) * 12
B = sin^-1((sin 16 / 10) * 12)
B ≈ 24.36°
Then, C = 180 - A - B ≈ 139.64°
Now we can use the Law of Sines again to solve for c:
sin A / a = sin C / c
sin 16 / 10 = sin 139.64 / c
c ≈ 20.97 or c ≈ 2.10 (due to the ambiguous case)
Therefore, the answer is B.

Given a =°16 , B =12 , and a =