#### Answer

$10\sqrt {2}$

#### Work Step by Step

From general properties of triangle
$\angle B=180-\left( \angle A+\angle C\right) =180-\left( 105+45\right) =30$
From the law of sines
$\dfrac {a}{\sin 45}=\dfrac {10}{\sin B}\Rightarrow a=\dfrac {10\sin 45}{\sin 30}=\dfrac {10\times \dfrac {\sqrt {2}}{2}}{\dfrac {1}{2}}=10\sqrt {2}$