#### Answer

$c \approx 600$ mile
$a \approx 416$ mile
$b \approx 431$ mile

#### Work Step by Step

1. Find the inertial angle of A by subtracting the external degrees from 180:
$\angle A = 180^{\circ} -84^{\circ} - 52^{\circ} = 44^{\circ}$
2. Find the distance of c by multiplying the speed by time
$c = 250 mph \times 2.4 h = 600$ miles
3. Use sine rule to find a
$\sin 44^{\circ} = \frac{a}{600}$
$a\approx 416$ miles
4. Use cosine rule to find b
$\cos 44^{\circ} = \frac{b}{600}$
$b\approx 431$ miles