Answer
The angles are $A=72.2^{\circ}, B=48.2^{\circ}$, and $C=59.6^{\circ}$
The angles are $A=107.8^{\circ}, B=48.2^{\circ}$, and $C=24.0^{\circ}$
Work Step by Step
We can use the law of sines to find the angle $A$:
$\frac{a}{sin~A} = \frac{b}{sin~B}$
$sin~A = \frac{a~sin~B}{b}$
$sin~A = \frac{(890~cm)~sin~(48.2^{\circ})}{697~cm}$
$A = arcsin(0.9519)$
$A = 72.2^{\circ}$
We can find angle $C$:
$A+B+C = 180^{\circ}$
$C = 180^{\circ}-A-B$
$C = 180^{\circ}-72.2^{\circ}-48.2^{\circ}$
$C = 59.6^{\circ}$
The angles are $A=72.2^{\circ}, B=48.2^{\circ}$, and $C=59.6^{\circ}$
Note that we can also construct another triangle.
$A = 180-72.2^{\circ} = 107.8^{\circ}$
We can find angle $C$:
$A+B+C = 180^{\circ}$
$C = 180^{\circ}-A-B$
$C = 180^{\circ}-48.2^{\circ}-107.8^{\circ}$
$C = 24.0^{\circ}$
The angles are $A=107.8^{\circ}, B=48.2^{\circ}$, and $C=24.0^{\circ}$
