Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. $a = 17 , b = 19 , C = 65 ^ { \circ }$
A) Law of Cosine; $A \approx 52.52 ^ { \circ } , B \approx 62.48 ^ { \circ } , c \approx 19.42$
B) Law of Sines; $A \approx 52.52 ^ { \circ } , B \approx 65 ^ { \circ } , c \approx 19$
C) Law of Sines; $A \approx 65 ^ { \circ } , B \approx 52.52 ^ { \circ } , c \approx 19$
D) Law of Sines; No solution
E) Law of Cosine; No solution

Question

Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. $a = 17 , b = 19 , C = 65 ^ { \circ }$ 
A) Law of Cosine; $A \approx 52.52 ^ { \circ } , B \approx 62.48 ^ { \circ } , c \approx 19.42$
B) Law of Sines; $A \approx 52.52 ^ { \circ } , B \approx 65 ^ { \circ } , c \approx 19$
C) Law of Sines; $A \approx 65 ^ { \circ } , B \approx 52.52 ^ { \circ } , c \approx 19$
D) Law of Sines; No solution
E) Law of Cosine; No solution

Quizplus · Accepted Answer

We need to use the Law of Cosines because we are given two side lengths and the included angle. Using the Law of Cosines, we can solve for the third side length and the other two angles. Solving for $c$ gives us $c \approx 19.42$. Then, using the Law of Cosines again, we can solve for the angles $A$ and $B$. We get $A \approx 52.52 ^ { \circ }$ and $B \approx 62.48 ^ { \circ }$, which means that the remaining angle is $C \approx 65 ^ { \circ }$. Therefore, the answer is A.

Determine Whether the Law of Sines or the Law of Cosines