#### Answer

$a = 10\sqrt 2$

#### Work Step by Step

1. Find $\angle B$
$\angle B = 180 - (\angle C + \angle A)$
$= 180 - (105 +45)$
$= 180 - 150$
$= 30^{\circ}$
2. Find $a$
$\frac{a}{sin(45)} = \frac{10}{sin(30)}$
$a = \frac{10sin(45)}{sin(30)}$
$a = \frac{10(\frac{\sqrt 2}{2})}{\frac{1}{2}}$
$a = \frac{2(10(\frac{\sqrt 2}{2}))}{1}$
$a = 2(10(\frac{\sqrt 2}{2}))$
$a = 2(\frac{10\sqrt 2}{2})$
$a = 2(5\sqrt 2)$
$a = 10\sqrt 2$