Answer:
[tex]c=9.3\ units[/tex]
Step-by-step explanation:
step 1
Find the measure of angle A
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]A+B+C=180^o[/tex]
substitute the given values
[tex]A+110^o+30^o=180^o\\A=40^o[/tex]
step 2
Find the length side c
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]
substitute the given values
[tex]\frac{12}{sin(40^o)}=\frac{c}{sin(30^o)}[/tex]
solve for c
[tex]c=\frac{12}{sin(40^o)}sin(30^o)[/tex]
[tex]c=9.3\ units[/tex]
