Geometry

Question Analysis

This question involves Ratio in Similar Shapes. The main focus is on leveraging the proportional relationship between the height of an object and the length of its shadow. Since the post and the flagpole are under the same lighting conditions, the triangles formed by the post, its shadow, and the light source, and the flagpole, its shadow, and the light source are similar, allowing us to use ratios to find the unknown height.

Key Concept Explanation:

The core concept is that in similar triangles, the ratios of corresponding sides are equal. Here, the ratio of the height of the post to the length of its shadow is the same as the ratio of the height of the flagpole to the length of its shadow. This property enables us to set up a proportion to solve for the unknown dimension.

Step-by-Step Solution

1. First, calculate the ratio of the height of the post to the length of its shadow. The post is 8 feet tall and its shadow is 6 feet long, so the ratio is .

2. Let the height of the flagpole be feet. Because the ratios of similar triangles are equal, we can establish the proportion .

3. Cross - multiply to solve for . We have

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