7. If $a$, $b$, $c$ are all real numbers, and for any real number $x$, the inequality $a \sin x + b \cos x + c > 0$ always holds, then the necessary and sufficient condition for $a$, $b$, $c$ is $\qquad$ .
7. $c>\sqrt{a^{2}+b^{2}}$.
$a \sin x + b \cos x = \sqrt{a^{2}+b^{2}} \sin (x+\varphi) \geqslant -\sqrt{a^{2}+b^{2}}$, to make $a \sin x + b \cos x + c > 0$ always true, it is sufficient that $-\sqrt{a^{2}+b^{2}} + c > 0, c > \sqrt{a^{2}+b^{2}}$. Conversely, if $c > \sqrt{a^{2}+b^{2}}$, then $a \sin x + b \cos x + c > a \sin x + b \cos x + \sqrt{a^{2}+b^{2}} = \sqrt{a^{2}+b^{2}}(\sin (x+\varphi) + 1) \geqslant 0, a \sin x + b \cos x + c > 0$ always holds. Therefore, the necessary and sufficient condition for $a, b, c$ is $c > \sqrt{a^{2}+b^{2}}$.