Final answer:
The shadow of the second 6-meter-tall pole would be 1.5 times the length of the 11-meter-long shadow cast by the 4-meter-tall first pole, resulting in a shadow length of 16.5 meters.
Step-by-step explanation:
Finding the Shadow Length of the Second Pole
To determine the length of the shadow cast by the second pole, we must recognize that the two poles and their respective shadows create similar triangles. Geometry and proportions play key roles in solving this problem.
The first pole, which is 4 meters tall, casts an 11-meter-long shadow. Given this information, we have two similar triangles – one involving the first pole and its shadow and another involving the second pole and its unknown shadow length.
The second pole is 6 meters tall, which is 1.5 times the height of the first pole (6m / 4m = 1.5). Because the triangles are similar, the shadow of the second pole will also be 1.5 times the length of the shadow of the first pole. So, the shadow length for the second pole is 11 meters times 1.5.
Shadow length of the second pole = 11m * 1.5 = 16.5 meters.