Answer
$\angle B \approx 110.0^{\circ}$
$a \approx 27.01$ m
$c \approx 21.36$ m
Work Step by Step
1. Find $\angle B$
$\angle B = 180 - (30.35 + 39.7)$
$= 180 - (70.05)$
$= 109.95^{\circ}$
$\approx 110.0^{\circ}$
2. Find $a$
$\frac{a}{sin(A)} = \frac{39.74}{sin(B)}$
$\frac{a}{sin(39.7)} = \frac{39.74}{sin(109.95)}$
$a = \frac{39.74sin(39.7)}{sin(109.95)}$
by GDC / calculator
$a = 27.005$ m
$a \approx 27.01$ m
3. Find $c$
$\frac{c}{sin(C)} = \frac{b}{sin(B)}$
$\frac{c}{sin(30.35)} = \frac{39.74}{sin(109.95)}$
$c = \frac{39.74sin(30.35)}{sin(109.95)}$
by GDC / calculator
$c = 21.3617...$ m
$c \approx 21.36$ m
