Answer
$A=27.90^{\circ}$.
$B=62.1^{\circ}$.
$b=27.57\;mi$.
Work Step by Step
The given values are
$a=14.6\;mi$
$c=31.2\;mi$.
By using trigonometric ratios.
$\frac{a}{c}=\sin{A}$
Isolate $A$.
$A=\sin^{-1}\left(\frac{a}{c} \right )$
Plug all values.
$A=\sin^{-1}\left(\frac{14.6\;mi}{31.2\;mi} \right )$
By using degree calculator simplify.
$A=27.90^{\circ}$ (rounded value).
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 $A$.
$B=90^{\circ}-27.90^{\circ}$
Simplify.
$B=62.1^{\circ}$.
By using Pythagorean theorem.
$b=\sqrt{c^2-a^2}$
Plug all values.
$b=\sqrt{(31.2\;mi)^2-(14.6\;mi)^2}$
Simplify.
$b=\sqrt{973.44\;mi^2-213.16\;mi^2}$
$b=\sqrt{(760.28\;mi^2)}$
$b=27.57\;mi$.
