Answer
$d=183.5m$
Work Step by Step
1) Find the radius $r$ the car's circular path must have for $v=34m/s$
We have $\tan\theta=\tan40$ and $g=9.8m/s^2$
$$\tan\theta=\frac{v^2}{rg}$$ $$r=\frac{v^2}{g\tan\theta}=140.58m$$
2) The figure below provides a way to find $d$ using $r$ and the given angle of the inclined plane. We can easily see that
$$d=\frac{r}{\cos40}=183.5m$$
