Final answer:
To find the length of the water slide, we can use trigonometry. The height of the slide is 11.5 feet and the angle it makes with the water surface is 40 degrees. By using the sine function, we can calculate the length of the slide.
Step-by-step explanation:
To find the length of the water slide, we can use trigonometry. The height of the slide is given as 11.5 feet and the angle it makes with the surface of the water is 40 degrees. We can use the sine function to calculate the length of the slide. The formula for sine is sin(theta) = opposite/hypotenuse. In this case, the opposite side is the height of the slide and the hypotenuse is the length of the slide.
Using the formula gives us sin(40 degrees) = 11.5 feet/hypotenuse. Rearranging the formula, we get hypotenuse = 11.5 feet / sin(40 degrees). Using a calculator, we find that sin(40 degrees) is approximately 0.6428. Dividing 11.5 feet by 0.6428 gives us a length of approximately 17.89 feet. Therefore, the water slide is approximately 17.89 feet long.