Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle.
A = 18,b = 20,C = 65°

A)Law of Sines;A ≈ 65°,B ≈ 52.79°,c ≈ 20
B)Law of Sines;A ≈ 52.79°,B ≈ 65°,c ≈ 20
C)Law of Cosines;A ≈ 52.79°,B ≈ 62.21°,c ≈ 20.49
D)Law of Sines;No solution
E)Law of Cosines;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 = 18,b = 20,C = 65°
​
A)Law of Sines;A ≈ 65°,B ≈ 52.79°,c ≈ 20
B)Law of Sines;A ≈ 52.79°,B ≈ 65°,c ≈ 20
C)Law of Cosines;A ≈ 52.79°,B ≈ 62.21°,c ≈ 20.49
D)Law of Sines;No solution
E)Law of Cosines;No solution

Quizplus · Accepted Answer

We can use the Law of Cosines to solve for side c:
c^2 = a^2 + b^2 - 2ab*cos(C)
c^2 = 18^2 + 20^2 - 2(18)(20)*cos(65°)
c ≈ 20.49

Then, we can use the Law of Sines to solve for angles A and B:
sin(A)/a = sin(C)/c 
sin(A)/18 = sin(65°)/20.49 
A ≈ 52.79°

sin(B)/b = sin(C)/c 
sin(B)/20 = sin(65°)/20.49 
B ≈ 62.21°

Therefore, the correct choice is C: Law of Cosines; A ≈ 52.79°, B ≈ 62.21°, c ≈ 20.49.

Determine Whether the Law of Sines or the Law of Cosine