Answer
$A = 49^{\circ}30'$
Work Step by Step
We can use the law of sines to find angle $A$:
$\frac{a}{sin~A} = \frac{c}{sin~C}$
$sin~A = \frac{a~sin~C}{c}$
$A = arcsin(\frac{a~sin~C}{c})$
$A = arcsin(\frac{(75.3~mm)~sin~79^{\circ}20'}{97.4~mm})$
$A = arcsin(0.7597)$
$A = 49.44^{\circ} = 49^{\circ}30'$
Note that another possible value for angle $A$ could be $180^{\circ}- 49^{\circ}30'$ which is $130^{\circ}30'$
However, then angle A and angle C sum to more than $180^{\circ}$ so this is not an acceptable value for angle A.
