#### Answer

$a = 0.6006~cm$
$b = 4.787~cm$
$\angle A = 7^{\circ}09'$

#### Work Step by Step

We can convert angle B to degrees:
$B = 82^{\circ}51' = (82+\frac{51}{60})^{\circ} = 82.85^{\circ}$
We can use angle B and angle C to find angle A:
$\angle A = 180^{\circ}-90^{\circ}-82.85^{\circ} = 7.15^{\circ}$
$\angle A = 7.15^{\circ}$ which is $7^{\circ}09'$
We can use angle B and $c$ to find $a$:
$cos~B = \frac{a}{c}$
$a = (c)~cos~B$
$a = (4.825~cm)~cos(82.85^{\circ})$
$a = 0.6006~cm$
We can use the Pythagorean theorem to find $b$:
$b^2 = c^2-a^2$
$b = \sqrt{c^2-a^2}$
$b = \sqrt{(4.825~cm)^2-(0.6006~cm)^2}$
$b = 4.787~cm$