Answer
$83.9 \ ft$
Work Step by Step
The trigonometric functions can be expressed as:
$\sin \theta=\dfrac{Opposite}{Hypotenuse} \\ \cos \theta=\dfrac{Adjacent}{Hypotenuse} \\ \tan \theta=\dfrac{Opposite}{Adjacent}$
We are given the angle and the adjacent side. Our aim is to compute the opposite side. So we use tangent.
Let $x$ be the opposite side.
Since, $\tan \theta=\dfrac{Opposite}{Adjacent}$
Therefore, $\tan (40^{\circ})=\dfrac{x}{100} \implies x \approx 83.9 \ ft$