Determine whether the Law of Sines or the Law of Cosines is needed to solve the tri- angle. Then solve the triangle. Round your answer to two decimal places.
$a = 154 , B = 10 ^ { \circ } , C = 5 ^ { \circ }$
A) Law of Cosines; No solution
B) Law of Sines; $A = 165 ^ { \circ } , b \approx 51.86 , c \approx 103.32$
C) Law of Sines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$
D) Law of Cosines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$
E) Law of Sines; 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. Round your answer to two decimal places. 
$a = 154 , B = 10 ^ { \circ } , C = 5 ^ { \circ }$ 
A) Law of Cosines; No solution
B) Law of Sines; $A = 165 ^ { \circ } , b \approx 51.86 , c \approx 103.32$
C) Law of Sines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$
D) Law of Cosines; $A = 165 ^ { \circ } , b \approx 103.32 , c \approx 51.86$
E) Law of Sines; No solution

Quizplus · Accepted Answer

The sum of angles in a triangle is 180°, so $A = 180° - 10° - 5° = 165°$. Use the Law of Sines to find sides $b$ and $c$: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. Solving gives $b \approx 103.32$ and $c \approx 51.86$.

Determine Whether the Law of Sines or the Law of Cosines