Trigonometry - Applications of Trigonometric Ratios

Mr Thomas is designing a toddler slide for a children amusement park.
The safety requirement of the toddler slide is as follows:

The manufacturing company charges \(\$7.50\) for every \(10\) cm of the length of slide made.
Calculate the difference in the cost of the slide if the minimum angle instead of the maximum angle is used. Give your answer in the nearest dollars.[6]

Editorial note: the prompt gives only a maximum height, not the chosen height. The numerical answer below assumes both designs use the full \(5\text{ ft}\) height and cost is proportional to length. Without a chosen common height, the cost difference is not uniquely determined.