Answer
The length of the slide is $~~10~m$
Work Step by Step
We can find the angle $\theta$ that is subtended by the slide:
$cos~\theta = \frac{8.0~m}{12~m}$
$\theta = cos^{-1}~\frac{8.0~m}{12~m}$
$\theta = 48.2^{\circ}$
We can find the length of the slide:
$L = \frac{48.2^{\circ}}{360^{\circ}}~(2\pi)(12~m)$
$L = 10~m$
The length of the slide is $~~10~m$
