Relating trigonometry to the Russian ice slides helps show students situations in which they might need to use the trigonometry they learn to find new information that they would otherwise not be able to find. It is impossible to go back in time and measure how long the slides were, but we can find a rough estimate through the use of trigonometry.
Having students do an activity where they design their own roller coaster can make learning about polynomials and their roots fun. Students could change up their equation as much as they’d like to try to get the roller coaster they want.