Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle.
A = 9,c = 6,B = 50°

A)Law of Sines;A ≈ 88.21°,C ≈ 41.79°,b ≈ 6.9
B)Law of Cosines;A ≈ 88.21°,C ≈ 41.79°,b ≈ 6.9
C)Law of Cosines;A ≈ 41.79°,C ≈ 88.21°,b ≈ 6.9
D)Law of Sines;A ≈ 41.79°,C ≈ 88.21°,b ≈ 6.9
E)Law of Sines;No solution

Question

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​
A = 9,c = 6,B = 50°
​
A)Law of Sines;A ≈ 88.21°,C ≈ 41.79°,b ≈ 6.9
B)Law of Cosines;A ≈ 88.21°,C ≈ 41.79°,b ≈ 6.9
C)Law of Cosines;A ≈ 41.79°,C ≈ 88.21°,b ≈ 6.9
D)Law of Sines;A ≈ 41.79°,C ≈ 88.21°,b ≈ 6.9
E)Law of Sines;No solution

Quizplus · Accepted Answer

We need to use the Law of Cosines since we have two sides (A and c) and their included angle (B). Using the Law of Cosines, we get:
b^2 = a^2 + c^2 - 2ac cos(B)
b^2 = 9^2 + 6^2 - 2(9)(6)cos(50°)
b ≈ 6.9
Now, we can use the Law of Sines to find angles A and C:
sin(A)/9 = sin(50°)/6.9
sin(A) ≈ 0.851
A ≈ 55.2°
C ≈ 180° - A - B ≈ 74.8°
Therefore, the answer is B.

Determine Whether the Law of Sines or the Law of Cosine