Answer
$B=37.9^{\circ}$.
$b=56.1\;mm$.
$c=91.2\;mm$.
Work Step by Step
The given values are
$A=52.1^{\circ}$
$a=72.0\;mm$.
In a right angle triangle sum of other two angles is $90^{\circ}$.
$A+B=90^{\circ}$
Isolate $B$.
$B=90^{\circ}-A$
Plug value of $A$.
$B=90^{\circ}-52.1^{\circ}$
Simplify.
$B=37.9^{\circ}$.
By using trigonometric ratios.
$\frac{a}{c}=\sin{A}$
Isolate $c$.
$c=\frac{a}{\sin{A}}$
Plug all values.
$c=\frac{72.0\;mm}{\sin{(52.1^{\circ})}}$
By using degree calculator simplify.
$c=91.2\;mm$ (rounded value).
By using trigonometric ratios.
$\frac{a}{b}=\tan{A}$
Isolate $b$.
$b=\frac{a}{\tan{A}}$
Plug all values.
$b=\frac{72.0\;mm}{\tan{(52.1^{\circ})}}$
By using degree calculator simplify.
$b=56.1\;mm$ (rounded value).
