7. If $a$, $b$, $c$ are all integers $(0<c<90)$, and satisfy $\sqrt{9-8 \sin 50^{\circ}}=a+b \sin c^{\circ}$. Then the value of $\frac{a+b}{c}$ is
7. $\frac{1}{2}$.

Notice that
$$
\begin{array}{l}
9-8 \sin 50^{\circ} \\
=9+8 \sin 10^{\circ}-8 \sin 10^{\circ}-8 \sin 50^{\circ} \\
=9+8 \sin 10^{\circ}-8\left[\sin \left(30^{\circ}-20^{\circ}\right)+\sin \left(30^{\circ}+20^{\circ}\right)\right] \\
=9+8 \sin 10^{\circ}-8 \cos 20^{\circ} \\
=9+8 \sin 10^{\circ}-8\left(1-2 \sin ^{2} 10^{\circ}\right) \\
=16 \sin ^{2} 10^{\circ}+8 \sin 10^{\circ}+1=\left(4 \sin 10^{\circ}+1\right)^{2} .
\end{array}
$$

Therefore, $a=1, b=4, c=10$. Hence $\frac{a+b}{c}=\frac{1}{2}$.