Final answer:
To determine the height of the flagpole, we use proportional relationships. Evan's height to his shadow's length is set equal to the flagpole's height to its shadow's length, which yields a flagpole height of approximately 21.33 feet.
Step-by-step explanation:
The student's question involves finding the height of a flagpole using the proportions set up by similar triangles created by the shadows. Since Evan's height and shadow length form a proportional relationship with the flagpole's height and shadow length, we can solve the problem using a simple ratio.
Let's denote Evan's height as E, Evan's shadow length as SE, the flagpole's height as F, and the flagpole's shadow length as SF. The relationship can be expressed as a proportion: E/SE = F/SF.
Plugging in the known values gives us 6 ft (Evan's height) / 9 ft (Evan's shadow) = F (flagpole's height) / 32 ft (flagpole's shadow). Cross-multiplying and solving for F yields F = (6 x 32) / 9.
Therefore, the flagpole's height F is 21.33 feet. So, using the proportions of the shadows and heights, we determined that the flagpole is approximately 21.33 feet tall.