In a tidal river, the time between high tide and low tide is

Last updated: 7/20/2022

In a tidal river, the time between high tide and low tide is 6.2 hours. At high tide the depth of the water is 23.4 feet, while at low tide the depth is 11.6 feet. Assume the water depth is a trigonometric function of time and assume low tide occurs at noon ($t=0$). A boat requires a depth of 14 feet to sail, and is docked at noon. If the captain wants to leave the dock as soon as possible, how many hours after noon can the boat set sail? Give your answer as a decimal rounded to 2 places after the decimal point.