Answer:
Option b
Step-by-step explanation:
To solve this problem use the law of the sines.
We have 2 angles of the triangle and one of the sides.
[tex]a = 4.6\\B = 19\°\\A = 92\°\\C = 180 -A - B\\C = 180 - 92 - 19\\C = 69\°[/tex]
The law of the sines is:
[tex]\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}[/tex]
Then:
[tex]\frac{sin(92)}{4.6} = \frac{sin(19)}{b}\\\\b = \frac{sin(19)}{\frac{sin(92)}{4.6}}\\\\b = 1.5[/tex]
[tex]\frac{sin(B)}{b} = \frac{sin(C)}{c}\\\\\frac{sin(19)}{1.5} = \frac{sin(69)}{c}\\\\c = \frac{sin(69)}{\frac{sin(19)}{1.5}}\\\\c = 4.30[/tex]
