Answer
The angles are $A=45.40^{\circ}, B=113.72^{\circ}$, and $C=20.88^{\circ}$
Work Step by Step
We can use the law of sines to find the angle $A$:
$\frac{b}{sin~B} = \frac{a}{sin~A}$
$sin~A = \frac{a~sin~B}{b}$
$sin~A = \frac{(189.6~yd)~sin~(113.72^{\circ})}{243.8~yd}$
$sin~A = 0.712$
$A = arcsin(0.712)$
$A = 45.40^{\circ}$
We can find angle $C$:
$A+B+C = 180^{\circ}$
$C = 180^{\circ}-A-B$
$C = 180^{\circ}-45.40^{\circ}-113.72^{\circ}$
$C = 20.88^{\circ}$
The angles are $A=45.40^{\circ}, B=113.72^{\circ}$, and $C=20.88^{\circ}$
