Final answer:
The length of the shadow cast by a 33-meter tall tetherball pole, when it's proportional to its height, would be 33 meters.
Step-by-step explanation:
The question pertains to the concept of similar triangles in geometry. When objects cast shadows due to sunlight or another source, the lengths of the shadows are proportional to the heights of the objects if the sun's rays are considered parallel. In this case, we are given a tetherball pole of height 33 meters and are asked to determine the length of its shadow if it's proportional to its height.
Since the question mentions that the length of the shadow is proportional to the height of the pole, the only length that is equal to the height of the object itself is option d) 33 meters. Therefore, the length of the shadow cast by a 33-meter tall tetherball pole would also be 33 meters if the shadow length is proportional to the object's height.