Answer
$\angle B = 49.2˚$
$a = 18.8$ cm
$c = 43.2$ cm
Work Step by Step
1. Find $\angle B$
$\angle B = 180 - (\angle A+ \angle C)$
$= 180 - (24.7 + 106.1)$
$= 180 - 130.8$
$= 49.2˚$
2. Find $a$
$\frac{a}{sin(24.7)} = \frac{34}{sin(49.2)}$
$a = \frac{34sin(24.7)}{sin(49.2)}$
by GDC / calculator
$a = 18.768...$
$a = 18.8$ cm
3. Find $c$
$\frac{c}{sin(106.1)} = \frac{34}{sin(49.2)}$
$a = \frac{34sin(106.1)}{sin(49.2)}$
by GDC / calculator
$c = 43.1528...$
$c = 43.2$ cm
