Answer
$B=50.3^{\circ}$.
$a=41.2\;km$.
$c=64.5\;km$.
Work Step by Step
The given values are
$A=39.7^{\circ}$
$b=49.6\;km$.
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 $A$.
$B=90^{\circ}-39.7^{\circ}$
Simplify.
$B=50.3^{\circ}$.
By using trigonometric ratios.
$\frac{b}{c}=\cos{A}$
Isolate $c$.
$c=\frac{b}{\cos{A}}$
Plug all values.
$c=\frac{49.6\;km}{\cos{(39.7^{\circ})}}$
By using degree calculator simplify.
$c=64.5\;km$ (rounded value).
By using trigonometric ratios.
$\frac{a}{b}=\tan{A}$
Isolate $a$.
$a=b\cdot \tan{A}$
Plug all values.
$a=(49.6\;km)\cdot \tan{(39.7^{\circ})}$
By using degree calculator simplify.
$a=41.2\;km$ (rounded value).
