Solving Problems Involving the Sine Function

In some cities, such as Niagara Falls or London, a Ferris wheel is installed to offer a panoramic view to tourists.

To climb inside the Ferris wheel, there is a platform installed at a height equivalent to half of the height of the Ferris wheel. To avoid collisions with bystanders, the lowest point of the Ferris wheel is |5 \ \text{m}| above the ground. At the summit, the passengers find themselves at an impressive height of |131\ \text{m}.| As soon as the passengers board, the carriage where the passengers are seated descends.

Given that the view becomes particularly spectacular from an altitude of |120\ \text{m}| and the Ferris wheel takes |32\ \text{minutes}| to complete a full turn, how long will tourists be in awe of the scenery?

The sine function was used here because the situation began on the midline.

If the starting point was a maximum or a minimum, the cosine function would have been a better choice.