Answer
$A=14.35^{\circ}$.
$a=22.99\;km$.
$b=89.86\;km$.
Work Step by Step
The given values are
$B=75.65^{\circ}$
$c=92.75\;km$.
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 $B$.
$A=90^{\circ}-75.65^{\circ}$
Simplify.
$A=14.35^{\circ}$.
By using trigonometric ratios.
$\frac{a}{c}=\cos{B}$
Isolate $a$.
$a={c}\cdot {\cos{B}}$
Plug all values.
$a={(92.75\;km)}\cdot {\cos{(75.65^{\circ})}}$
By using degree calculator simplify.
$a=22.99\;km$ (rounded value).
By using trigonometric ratios.
$\frac{b}{c}=\sin{B}$
Isolate $a$.
$b={c}\cdot {\sin{B}}$
Plug all values.
$b={(92.75\;km)}\cdot {\sin{(75.65^{\circ})}}$
By using degree calculator simplify.
$b=89.86\;km$ (rounded value).
