Yes, trigonometric ratios can make roller coasters and amusement rides better! Designers use these ratios to figure out angles, heights, and lengths of different parts of the rides.

Here are some examples:

• Height Calculations: Let’s say there’s a drop at a $30^\circ$ angle, and the drop is 50 meters straight down. You can find out how far it goes sideways using the formula $\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}}$.

• Safety Designs: Designers make sure that turns are safe. They need to know how much force is needed to keep riders on the track. They use a formula called $F = \frac{mv^2}{r}$, where $r$ (the radius) is related to angles that they find with sine and cosine.

These ways of using math help to create exciting and safe rides!