Final answer:
To find the height of the ramp, we use the sine function with the given angle of 9 degrees and the length of the 33-ft ramp. The calculation gives 5.2 ft when rounded to one decimal place, yet this is not listed among the options. The closest given option to our calculation is 5.7 ft.
Step-by-step explanation:
To find the height of the ramp above the water at the ramp's highest point, we need to use trigonometry, specifically the sine function, which relates the opposite side of a right-angled triangle (in this case, the height of the ramp) to the hypotenuse (the length of the ramp).
The sine of an angle in a right-angled triangle is equal to the opposite side divided by the hypotenuse:
sin(\(\theta\)) = opposite/hypotenuse
With a 33-ft ramp making a 9-degree angle with the water, the calculation would be:
sin(9\(^{\circ}\)) = height/33 ft
Therefore, to find the height:
height = 33 ft * sin(9\(^{\circ}\))
After calculating, we get:
height ≈ 33 ft * 0.1564
height ≈ 5.1612 ft
When rounded to one decimal place, the height is 5.2 ft, which is not provided in the options, so there seems to be an error in the given options. The result closest to our calculation would be Option a) 5.7 ft.