Final answer:
The distance from Stephan's eyes to the band of shale cannot be determined with the given information.
Step-by-step explanation:
The distance D to the horizon can be calculated using the formula D = 112.88 km x √h, where h is the height above the ground in kilometers. In this case, Stephan is standing on a mesa, which is a type of elevated landform. The question does not provide the specific height of the mesa, so we cannot calculate the distance to the band of shale from his eyes using the given information. Therefore, we cannot determine the approximate distance from Stephan's eyes to the band of shale.