Answer:
B
Step-by-step explanation:
Use the Law of Cosines to find the measure of segment c:
[tex]c=\sqrt{a^2+b^2-2ab*cos(C)}\\\\c=\sqrt{12^2+13^2-2(12)(13)*cos(134)}\\\\c=\sqrt{313-312cos(134)}\\\\c=\sqrt{313-312(-.6946583705)}\\\\c=\sqrt{313-(-216.7334116)}\\\\c=\sqrt{313+216.7334116}\\\\c=\sqrt{529.7334116}\\[/tex]
c ≈ 23.01593821 km ≈ 23 km
Since c = 23 km, our only options are choices B and D. Now, let's find the measure of angle A to confirm. To do this we will use the Law of Sines:
[tex]\frac{sin(A)}{a} =\frac{sin(C)}{c} \\\\\frac{sin(A)}{12}=\frac{sin(134)}{23.01593821}\\\\sin(A)=12(\frac{sin(134)}{23.01593821})\\\\A=sin^{-1}[12(\frac{sin(134)}{23.01593821})]\\\\[/tex]
A ≈ 22.02726885° ≈ 22°
Since the measure of c = 23 km and the measure of angle A = 22°, the answer must be choice B.
