Answer
$a =122.88 \hspace{1pt}km$
$B=25.111^\circ$
$C=30.222^\circ$
Work Step by Step
$a^2 = b^2+c^2-2ac \cos{A^\circ} \\= (63.4)^2+(75.2)^2-2 \times 63.4 \times 75.2 \cos{124.667^\circ}= 15098$
$$a = \boxed{122.88 \hspace{1pt} km}$$
$\cos{B} = \dfrac{a^2+c^2-b^2}{2ac} = \dfrac{(122.88)^2+(75.2)^2-(63.4)^2}{2 \times 122.88 \times 75.2} = 0.9055$
$$\therefore B =\boxed{25.111^\circ} $$
$$C = 180-(A+B) = 180-(124.667+25.111) = \boxed{30.222^\circ}$$
