Answer
$A = 92˚$
$b \approx 6.1$ m
$c \approx 3.8$ m
Work Step by Step
1. Solve for the unknown angle $A$
$A + 57 + 31 = 180$
$A + 88 = 180$
$A = 92˚$
2. Solve for the missing length $b$
$\frac{b}{sin(57)} =\frac{7.3}{sin(92)}$
$b = \frac{7.3sin(57)}{sin(92)}$
by GDC / calculator
$b = \frac{6.12...}{0.999...}$
$b = 6.1260...$ m
$b \approx 6.1$ m
3. Solve for the missing length $c$
$\frac{c}{sin(31)} =\frac{7.3}{sin(92)}$
$c = \frac{7.3sin(31)}{sin(92)}$
by GDC / calculator
$c = \frac{3.759...}{0.999...}$
$c = 3.762....$ m
$c \approx 3.8$ m