Answer
The angles are $A=112^{\circ}10', B=26^{\circ}30'$, and $C=41^{\circ}20'$
Work Step by Step
We can use the law of sines to find the angle $B$:
$\frac{c}{sin~C} = \frac{b}{sin~B}$
$sin~B = \frac{b~sin~C}{c}$
$sin~B = \frac{(25.9~m)~sin~(41.33^{\circ})}{38.4~m}$
$B = arcsin(0.4454)$
$B = 26^{\circ}30'$
We can find angle $A$:
$A+B+C = 180^{\circ}$
$A = 180^{\circ}-B-C$
$A = 180^{\circ}-26^{\circ}30'-41^{\circ}20'$
$A = 112^{\circ}10'$
The angles are $A=112^{\circ}10', B=26^{\circ}30'$, and $C=41^{\circ}20'$
