Answer
$B=58.8^{\circ}$.
$b=102 \;m$.
$c=119 \;m$.
Work Step by Step
Given values are
one leg $a=61.7\;m$.
$A=31.2^{\circ}$
In a right angle triangle sum of the other two angles is equal to $90^{\circ}$.
$A+B=90^{\circ}$
Isolate $B$.
$B=90^{\circ}-A$
Plug value of $A$.
$B=90^{\circ}-31.2^{\circ}$
Simplify.
$B=58.8^{\circ}$
By using trigonometric ratios.
$\frac{a}{c}=\sin{A}$
Isolate $c$.
$c=\frac{a}{\sin{A}}$
Plug all values.
$c=\frac{61.7}{\sin{(31.2^{\circ})}}$
Simplify.
$c=119 \;m$ (rounded value).
By using trigonometric ratios.
$\frac{a}{b}=\tan{A}$
Isolate $b$.
$b=\frac{a}{\tan{A}}$
Plug all values.
$b=\frac{61.7\;m}{\tan{(31.2^{\circ})}}$
Simplify.
$b=102 \;m$ (rounded value).
