1-110 Given the line $a x+b y+c=0$ where the coefficients $a, b, c$ are 3 different elements chosen from the set $\{-3,-2,-1,0,1,2,3\}$, and the inclination angle of the line is acute. Find the number of all such different lines.
[Solution] Let the inclination angle of the line be $\theta$, then $\theta$ is an acute angle, so $\operatorname{tg} \theta=-\frac{a}{b}>0$. Without loss of generality, assume $a>0, b<0$.
(1) When $c=0$, $a$ has 3 possible values, and $b$ also has 3 possible values. Since $3 x-3 y=0$, $2 x-2 y=0$ and $x-y=0$ are the same line, we should remove two duplicate lines. Therefore, there are $3 \times 3-2=7$ such lines.
(2) When $c \neq 0$, $a$ has 3 possible values, $b$ has 3 possible values, and $c$ has 4 possible values. It is easy to see that any two lines are different, so there are $3 \times 3 \times 4=36$ such lines.
In summary, there are a total of 43 lines that meet the requirements.