Answer
$\sqrt 3$
Work Step by Step
Sum of Internal angles of triangle is $180^0$
Then
$\angle C=180-\left( 60+75\right) =45$
From the laws of sines
$\dfrac {\sqrt {2}}{\sin \angle C}=\dfrac {a}{\sin 60}\Rightarrow a=\dfrac {\sqrt {2}\times \sin 60}{\sin 45}=\dfrac {\sqrt {2}\times \dfrac {\sqrt {3}}{2}}{\dfrac {\sqrt {2}}{2}}=\sqrt {3}
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