Answer
$A=30^{\circ} $.
$B=60^{\circ}$.
$b=117.78\;mi$.
Work Step by Step
Given values are
One leg $a=68.0\;mi$.
Hypotenuse $c=136\;mi$.
By using trigonometric ratios.
$\sin{A}=\frac{a}{c}$
Isolate $A$.
$A=\sin^{-1}\left (\frac{a}{c}\right )$
Plug all values.
$A=\sin^{-1}\left (\frac{68.0\;mi}{136\;mi}\right )$
Simplify.
$A=30^{\circ} $ (rounded value).
In a right angle triangle sum:
$A+B=90^{\circ}$
Isolate $B$.
$B=90^{\circ}-A$
Plug value of $A$.
$B=90^{\circ}-30^{\circ}$
Simplify.
$B=60^{\circ}$.
By using the Pythagorean theorem.
$b=\sqrt{c^2-a^2}$
Plug all values.
$b=\sqrt{(136\;mi)^2-(68.0\;mi)^2}$
Simplify.
$b=\sqrt{18496\;mi^2-4624\;mi^2}$
$b=117.78\;mi$.
