Answer
$$b=38km$$
$$c=42.6km$$
Work Step by Step
To find side b, we can use the trigonometric ratio for tangent
$tanB=\frac{b}{a}$
Where
$B=63.2°$
$a=19.2km$
Solving for b we get:
$b=a*tanB$
$b=19.2km*tan(63.2°)$
$b=19.2km*1.9797$
$b=38km$
To find side c (the hypotenuse), we can use the trigonometric ratio for cosine.
$cosB=\frac{a}{c}$
Where
$B=63.2°$
$a=19.2km$
Solving for c we get:
$c=\frac{a}{cosB}$
$c=\frac{19.2km}{cos(63.2°)}$
$c=\frac{19.2km}{0.4509}$
$c=42.6km$
