Use the law of Cosines to solve the given triangle. Round your answer to two decimal places. $$a = 13 , b = 17 , c = 23$$
A) $A \approx 33.92 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 99.24 ^ { \circ }$
B) $A \approx 46.84 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 86.32 ^ { \circ }$
C) $A \approx 33.92 ^ { \circ } , B \approx 99.24 ^ { \circ } , C \approx 46.84 ^ { \circ }$
D) $A \approx 99.24 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 33.92 ^ { \circ }$
E) $A \approx 46.84 ^ { \circ } , B \approx 33.92 ^ { \circ } , C \approx 99.24 ^ { \circ }$

Question

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places. $$a = 13 , b = 17 , c = 23$$ 
A) $A \approx 33.92 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 99.24 ^ { \circ }$
B) $A \approx 46.84 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 86.32 ^ { \circ }$
C) $A \approx 33.92 ^ { \circ } , B \approx 99.24 ^ { \circ } , C \approx 46.84 ^ { \circ }$
D) $A \approx 99.24 ^ { \circ } , B \approx 46.84 ^ { \circ } , C \approx 33.92 ^ { \circ }$
E) $A \approx 46.84 ^ { \circ } , B \approx 33.92 ^ { \circ } , C \approx 99.24 ^ { \circ }$

Quizplus · Accepted Answer

Using the Law of Cosines, we have:
$$a^2=b^2+c^2-2bc\cos A$$
$$13^2=17^2+23^2-2\cdot17\cdot23\cos A$$
$$169=858-782\cos A$$
$$\cos A= \frac{347}{391}$$
$$A \approx 33.92^{\circ}$$
Now we can use Law of Sines to find B and C:
$$\frac{\sin B}{17}=\frac{\sin A}{13}$$
$$\sin B = \frac{17\sin A}{13}$$
$$\sin B \approx 0.5528$$
$$B \approx 33.92^{\circ} \text{(by symmetry)} \text{  or } B \approx 146.08^{\circ}$$
Since Β+Γ must be less than 180°, we have
$$C \approx 180^{\circ} - A - B \approx 99.24^{\circ}$$
Thus, the answer is A.

Use the Law of Cosines to Solve the Given Triangle a=13,b=17,c=23a = 13 , b = 17 , c = 23a=13,b=17,c=23

Use the Law of Cosines to Solve the Given Triangle $a = 13 , b = 17 , c = 23$