Final answer:
By using the concept of similar triangles, we can determine that the length of the maypole's shadow, when compared to a nearby pine tree, is 6 yards long.
Step-by-step explanation:
Similar Triangles in Shadow Problems
To determine the length of the maypole's shadow, we use the concept of similar triangles. The pine tree and its shadow form a right triangle, and similarly, the maypole and its shadow will also form a right triangle with the same angles since the Sun's rays are parallel. The relationship between the height of objects and the length of their shadows is proportional when the Sun's angle is the same.
The pine tree's height is 12 yards and its shadow is 9 yards long. Using a proportion, where the height of the first object is to its shadow length as the height of the second object is to its unknown shadow length, we can set up the following equation:
12 yards / 9 yards = 8 yards / x yards
Now we cross-multiply and solve for x:
12x = 72
Dividing both sides by 12:
x = 6 yards
Therefore, the maypole's shadow is 6 yards long.