I have a triangle like this and I must find the length of the unkown side with question mark:
And I am using law of sines like this:
$$ \dfrac{\sin 55^\circ}{2} = \dfrac{\sin 35^\circ}{x} $$ then we got this equation $$ x = \dfrac{2\sin 35^\circ}{\sin 55^\circ} $$ and it gives me the answer $ x \approx 1.40 $
But when I use this equation:
$$ \tan 35^\circ = \dfrac{x}{2} $$ $$ x = \dfrac{2}{\tan 35^\circ} $$
I get this answer: $ x \approx 2.85 $
Did I miss something?

You're last step is incorrect.
$$\tan 35^\circ = \frac{x}{2}$$
is equivalent to
$$x = 2 \tan 35^\circ$$
which does give the same result.