Answer:
A = [tex]75^o[/tex], a = 9.4 , and b = 7.5 (which coincides with option C among the listed possible answers)
Step-by-step explanation:
First, we can find the length of side b through the law if sines:
[tex]\frac{b}{sin(B)} = \frac{c}{sin(C)}\\b=\frac{c\,*\,sin(B)}{sin(C)}\\ b=\frac{8\,*\,sin(50^o)}{sin(55^o)}\\b=7.481[/tex]
That we can round to 7.5
Now we can find angle A using the property that the addition of all angles in a triangle must equal [tex]180^o[/tex]:
[tex]A+B+C=180^o\\A+50^o+55^o=180^o\\A=180^o-50^o-55^o\\A=75^o[/tex]
And finally, we can find side "a" by using again the law of sines:
[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}\\a=\frac{c\,*\,sin(A)}{sin(C)}\\ a=\frac{8\,*\,sin(75^o)}{sin(55^o)}\\a=9.4334[/tex]
which can be rounded to a = 9.4
