Answer
$\angle C= 78.4˚$
$a = 26.5$ cm
$b = 38.3$ cm
Work Step by Step
1. Find $\angle C$
$\angle C = 180 - (\angle B + \angle A)$
$= 180 - (101.6)$
$= 78.4˚$
2. Find $a$
$\frac{a}{sin(38.2)} = \frac{42}{sin(78.4)}$
$a = \frac{42sin(38.2)}{sin(78.4)}$
by GDC / calculator
$a = 26.514...$
$a = 26.5$ cm
3. Find $b$
$\frac{b}{sin(63.4)} = \frac{42}{sin(78.4)}$
$b = \frac{42sin(63.4)}{sin(78.4)}$
by GDC / calculator
$b = 38.337...$
$b = 38.3$ cm
