Answer
$\angle A = 65.6^{\circ}$
$c \approx 2.727$ cm
$b \approx 1.942$ cm
Work Step by Step
1. Find $\angle A$
$\angle A = 180 - (\angle B + \angle C)$
$= 180 - (42.57+71.83)$
$= 180 - 114.4$
$= 65.6^{\circ}$
2. Find $b$
$\frac{b}{sin(B)} = \frac{a}{sin(A)}$
$\frac{b}{sin(42.57)} = \frac{2.614}{sin(65.6)}$
$b = \frac{2.614sin(42.57)}{sin(65.6)}$
by GDC / calculator
$b = 1.94177...$
$b \approx 1.942$ cm
3. Find $c$
$\frac{c}{sin(C)} = \frac{a}{sin(A)}$
$\frac{c}{sin(71.83)} = \frac{2.614}{sin(65.6)}$
$c = \frac{2.614sin(71.83)}{sin(65.6)}$
by GDC / calculator
$c = 2.72724...$
$c \approx 2.727$ cm
