Answer
There is one triangle that exists with the given parts.
$A = 25.5^{\circ}, B = 102.2^{\circ}$, and $C = 52.3^{\circ}$
$a = 32.5~yd, b = 73.9~yd$, and $c = 59.8~yd$
Work Step by Step
We can use the law of sines to find the angle $A$:
$\frac{c}{sin~C} = \frac{a}{sin~A}$
$sin~A = \frac{a~sin~C}{c}$
$sin~A = \frac{(32.5~yd)~sin~(52.3^{\circ})}{59.8~yd}$
$A = arcsin(0.43)$
$A = 25.5^{\circ}$
We can find angle $B$:
$A+B+C = 180^{\circ}$
$B = 180^{\circ}-A-C$
$B = 180^{\circ}-25.5^{\circ}-52.3^{\circ}$
$B = 102.2^{\circ}$
We can find the length of side $b$:
$\frac{b}{sin~B} = \frac{c}{sin~C}$
$b = \frac{c~sin~B}{sin~C}$
$b = \frac{(59.8~yd)~sin~(102.2^{\circ})}{sin~52.3^{\circ}}$
$b = 73.9~yd$
Note that we can also find another angle for A.
$A = 180-25.5^{\circ} = 154.5^{\circ}$
However, we can not form a triangle with this angle A and angle C since these two angles sum to more than $180^{\circ}$
