Final answer:
The height of the sailboat is determined by setting a proportion using the buoy's height and shadow. With the sailboat's shadow being 12 feet, a proportion with the buoy's measurements provides a sailboat height of 24 feet.
Step-by-step explanation:
To determine the height of the sailboat we will use the fact that similar triangles have proportional sides. The buoy, which is 2 feet tall, casts a 1-foot shadow. Therefore, for every foot of height, the shadow is half a foot. Using this ratio, we can determine the height of the sailboat by knowing that it casts a shadow of 4 yards, which is equivalent to 12 feet (since 1 yard is equal to 3 feet). If we set up the proportion with the buoy's measurements (2 feet tall and 1-foot shadow), the sailboat's measurements would be 'x' feet tall and 12 feet shadow. The proportion is 2/1 = x/12. Solving for 'x' gives us a height of 24 feet for the sailboat. Therefore, the correct answer is d. 24 feet.