From the story. The Christian Science Monitor's 1998 story says the boys taught themselves trigonometry to work out how far their launches went. Distance downrange is a projectile problem. (More in October Sky.)
When a flight leans, its speed splits into a sideways part, $v\cos\theta$, that stays the same (ignoring air), and an up-and-down part, $v\sin\theta$, that gravity slows and reverses. The time in the air comes from the vertical part; the range is the sideways speed times that time.
Key idea
On level ground with no drag: $$t = \frac{2v\sin\theta}{g}, \qquad R = \frac{v^2\sin 2\theta}{g}, \qquad H = \frac{(v\sin\theta)^2}{2g}.$$ Range is largest at $45^\circ$, and $\theta$ and $90^\circ - \theta$ give the same range. (Rockets are launched close to vertical, within $30^\circ$ under the NAR safety code, to keep them over the field.)
Worked example: Downrange
A ball leaves the ground at $25\ \text{m/s}$, $60^\circ$ up. Where does it land?
- $R = \dfrac{25^2\sin 120^\circ}{9.8} = \dfrac{625(0.866)}{9.8} \approx 55\ \text{m}$.
Answer: $\approx 55\ \text{m}$
Common mistake
Using the whole speed in both directions. Split it into $v\cos\theta$ and $v\sin\theta$ first.