Answer
$$a=13.6mi$$
$$b=34.1mi$$
Work Step by Step
To find side a, we can use the trigonometric ratio for cosine.
$cosB=\frac{a}{c}$
Where
$B=68.3°$
$c=36.7mi$
Solving for a we get:
$a=c*cosB$
$a=36.7mi*cos(68.3°)$
$a=36.7mi*0.3697$
$a=13.6mi$
To find side b, we can use the trigonometric ratio for sine.
$sinB=\frac{b}{c}$
Where
$B=68.3°$
$c=36.7mi$
Solving for b we get:
$b=c*sinB$
$b=36.7mi*sin(68.3°)$
$b=36.7mi*0.9291$
$b=34.1mi$
