Explanation:
hi, this looks complicated, however, let's deal with it.
using sine rule,
we have,
a/sin A= c/sin C
4.83/sin 46= 5.5/sin C
cross multiply
4.83sin C=5.5sin 46
sin C= (5.5sin46)/4.83
sin C= 0.8191
C=sin inverse of 0.8191
C=54.99 approximately 55
since we have C, we can now find B to get b or rather AC
A+B+C=180. (sum of angles in a triangle)
46°+ B + 54.99°=180°
B+ 100.99°=180°
B°=180°-100.99°
B=79°
since we have B, we can find b or rather AC
using cosine rule,
b²=c²+a²-2 x c x a x cos B
b²= 5.5² + 4.83² - 2 x 5.5 x 4.83 x cos 79°
b²=30.25+23.33-53.13cos79
b²=53.58-10.14
b²=43.44
b=6.59 approximately 6.6