Answer
The angles are $A=142.13^{\circ}, B=27.19^{\circ}$, and $C=10.68^{\circ}$
Work Step by Step
We can use the law of sines to find the angle $B$:
$\frac{b}{sin~B} = \frac{a}{sin~A}$
$sin~B = \frac{b~sin~A}{a}$
$sin~B = \frac{(5.432~ft)~sin~(142.13^{\circ})}{7.297~ft}$
$B = arcsin(0.457)$
$B = 27.19^{\circ}$
We can find angle $C$:
$A+B+C = 180^{\circ}$
$C = 180^{\circ}-A-B$
$C = 180^{\circ}-142.13^{\circ}-27.19^{\circ}$
$C = 10.68^{\circ}$
The angles are $A=142.13^{\circ}, B=27.19^{\circ}$, and $C=10.68^{\circ}$
Note that we can also find another value for angle B.
$B = 180-27.19^{\circ} = 152.81^{\circ}$
However, we can not form a triangle with this angle B and angle A since these two angles sum to more than $180^{\circ}$
