ANSWER:
Triangle 1:
A = 35.69°
C = 114.31°
c = 10.94
Triangle 2:
A = 144.31°
C = 5.69°
c = 1.19
STEP-BY-STEP EXPLANATION:
Given:
B = 30°, b = 6, a = 7
We calculate the angle A by means of the law of sines:
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \\ \text{ We replacing} \\ \\ \frac{7}{\sin A}=\frac{6}{\sin30} \\ \\ \sin A=\frac{7}{6}\cdot\sin30 \\ \\ \sin A=\frac{7}{12} \\ \\ A=\sin^{-1}\left(\frac{7}{12}\right)\: \\ \\ A_{acute}=35.69\degree \\ \\ A_{obtuse}=144.31\degree \end{gathered}[/tex]We calculate the value of angle C, knowing that the sum of all internal angles is equal to 180°
[tex]\begin{gathered} \text{ Acute} \\ \\ 180=35.69+30+C \\ \\ C=180-30-35.69=114.31\degree \\ \\ \text{ Obtuse} \\ \\ 180=144.31+30+C \\ \\ C=180-30-144.31=5.69\degree \end{gathered}[/tex]Side c is also calculated with the law of sines, like this:
[tex]\begin{gathered} \text{ Acute} \\ \\ \frac{b}{\sin B}=\frac{c}{\sin C} \\ \\ \frac{6}{\sin(30)}=\frac{c}{\sin114.31} \\ \\ c=\frac{6}{\sin(30)}\cdot\sin114.31 \\ \\ c=\:10.94 \\ \\ \text{ Obtuse} \\ \\ \frac{7}{\sin(A)}=\frac{c}{\sin(C)} \\ \\ c=\frac{6}{\sin(30)}\sin(5.69) \\ \\ c=1.19 \end{gathered}[/tex]Therefore;
Triangle 1:
A = 35.69°
C = 114.31°
c = 10.94
Triangle 2:
A = 144.31°
C = 5.69°
c = 1.19