Answer
$A=73.46°$
$B=16.54°$
$C=90°$
$a=52.88$
$b=15.70$
$c=55.16$
Work Step by Step
$c^2=a^2+b^2$
$55.16^2=a^2+15.70^2$
$a^2=55.16^2-15.70^2$
$a=\sqrt {55.16^2-15.70^2}=52.8785$
$sin~A=\frac{opp}{hyp}=\frac{a}{c}=\frac{52.8785}{55.16}$
$A=arcsin(\frac{52.8785}{55.16})=73.46°$
$sin~B=\frac{opp}{hyp}=\frac{b}{c}=\frac{15.70}{55.16}$
$B=arcsin(\frac{15.70}{55.16})=16.54°$
$C=90°$ because it is a right triangle.