Answer
$\angle A= 34.72^{\circ}$
$a \approx 3325$ ft
$c \approx 5701$ ft
Work Step by Step
1. Find $\angle A$
$\angle A = 180 - (\angle B + \angle C)$
$= 180 - (42.88 + 102.40)$
$= 180 - 145.28$
$= 34.72^{\circ}$
2. Find $a$
$\frac{a}{sin(A)} = \frac{b}{sin(B)}$
$\frac{a}{sin(34.72)} = \frac{3972}{sin(42.88)}$
$a = \frac{3972sin(34.72)}{sin(42.88)}$
by GDC / calculator
$a = 3324.664...$ ft
$a \approx 3325$ ft
3. Find $c$
$\frac{c}{sin(C)} = \frac{b}{sin(B)}$
$\frac{c}{sin(102.4)} = \frac{3972}{sin(42.88)}$
$c = \frac{3972sin(102.4)}{sin(42.88)}$
by GDC / calculator
$c = 5701.0156...$
$c \approx 5701$ ft
