Geometry

Question Analysis

This question involves Ratio in Similar Shapes. The main focus is on using the proportional relationship between the height of an object and the length of its shadow. Since the flagpole and the streetlamp are under the same lighting conditions, the triangles formed by the flagpole, its shadow, and the light source, and the streetlamp, its shadow, and the light source are similar. We can use the equality of ratios of corresponding sides of these similar triangles to find the height of the streetlamp.

Key Concept Explanation:

The key concept here is that for similar triangles, the ratios of corresponding sides are equal. In this context, the ratio of the height of the flagpole to the length of its shadow is the same as the ratio of the height of the streetlamp to the length of its shadow. This property allows us to set up a proportion to solve for the unknown height of the streetlamp.

Step-by-Step Solution

1. First, calculate the ratio of the height of the flagpole to the length of its shadow. The flagpole is 33 feet tall and its shadow is 22 feet long, so the ratio is .

2. Let the height of the streetlamp be feet. Because the triangles are similar, we can set up the proportion .

3. Cross - multiply to solve for . We get .

4. Calculate

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