#### Answer

$a = 306~m$
$b = 1248~m$
$B = 76^{\circ}12'$

#### Work Step by Step

We can convert angle A to degrees:
$A = 13^{\circ}47' = (13+\frac{47}{60})^{\circ} = 13.8^{\circ}$
We can use angle A and angle C to find angle B:
$B = 180^{\circ}-90^{\circ}-13.8^{\circ} = 76.2^{\circ}$
$B = 76.2^{\circ}$ which is $76^{\circ}12'$
We can use angle A and $c$ to find $b$:
$cos~A = \frac{b}{c}$
$b = (c)~cos~A$
$b = (1285~m)~cos(13.8^{\circ})$
$b = 1248~m$
We can use the Pythagorean theorem to find a:
$a^2 = c^2-b^2$
$a = \sqrt{c^2-b^2}$
$a = \sqrt{(1285~m)^2-(1248~m)^2}$
$a = 306~m$