Answer
$\frac{4\sqrt {61}}{13}~ft\approx2.4~ft$
Work Step by Step
A height of 18 feet is 5 feet above of the origin, that is, $y=5$
$x^2-\frac{3y^2}{169}=1$
$x^2-\frac{3(5)^2}{169}=1$
$x^2-\frac{75}{169}=1$
$x^2=\frac{75}{169}+1=\frac{244}{169}$
$x=±\frac{2\sqrt {61}}{13}$
Which gives us the points: $(±\frac{2\sqrt {61}}{13},5)$. The distance between these points is:
$\frac{2\sqrt {61}}{13}-(-\frac{2\sqrt {61}}{13})=\frac{4\sqrt {61}}{13}\approx2.4$
