Answer
$A=67.6^{\circ}$.
$a=42.53\;mi$.
$b=17.53\;mi$.
Work Step by Step
The given values are
$B=22.4^{\circ}$
$c=46.0\;mi$.
In a right angle triangle sum of other two angles is $90^{\circ}$.
$A+B=90^{\circ}$
Isolate $A$.
$A=90^{\circ}-B$
Plug value of $B$.
$A=90^{\circ}-22.4^{\circ}$
Simplify.
$A=67.6^{\circ}$.
By using trigonometric ratios.
$\frac{a}{c}=\cos{B}$
Isolate $a$.
$a={c}\cdot {\cos{B}}$
Plug all values.
$a={(46.0\;mi)}\cdot {\cos{(22.4^{\circ})}}$
By using degree calculator simplify.
$a=42.53\;mi$ (rounded value).
By using trigonometric ratios.
$\frac{b}{c}=\sin{B}$
Isolate $a$.
$b={c}\cdot {\sin{B}}$
Plug all values.
$b={(46.0\;mi)}\cdot {\sin{(22.4^{\circ})}}$
By using degree calculator simplify.
$b=17.53\;mi$ (rounded value).
