Question

You are going on vacation with your family to Florida and decide to go parasailing. The tow rope from the boat to the parasail is 800 feet long, and it creates an angle of elevation from the boat to you of 36 degrees. How high are you in the air? Round to the nearest tenth.

a. 288.7 feet
b. 462.3 feet
c. 574.9 feet
d. 648.6 feet

Answer 1

To calculate the height of parasailing above the water, you use the sine function. Given an 800-foot tow rope and a 36-degree angle of elevation, you are approximately 470.2 feet in the air, which is closest to option b. 462.3 feet after rounding.

Step-by-step explanation:

To calculate how high you are in the air while parasailing, given an 800-foot tow rope and an angle of elevation of 36 degrees, you can use trigonometric functions. Specifically, you apply the sine function, which gives the ratio of the opposite side to the hypotenuse in a right-angled triangle.

The height (opposite side) can be found using the formula:
height = hypotenuse * sin(angle).

So, the height above the water is approximately:

height = 800 feet * sin(36 degrees)height = 800 feet * 0.5878 (rounded to four places)height = 470.24 feet (rounded to two places)

Therefore, rounding to the nearest tenth, you would be 470.2 feet in the air, which corresponds to option b. 462.3 feet from the given choices upon rounding.