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 streetlight and the tower are in the same lighting conditions, the triangles formed by them, their shadows, and the lines of light are similar, allowing us to find the height of the tower by setting up a ratio.

Key Concept Explanation:

The key concept is that similar triangles have equal ratios of corresponding sides. Here, the ratio of the height of the streetlight to the length of its shadow is identical to the ratio of the height of the tower to the length of its shadow. This property enables us to establish a proportion to solve for the unknown height.

Step-by-Step Solution

1. First, determine the ratio of the height of the streetlight to the length of its shadow. The streetlight is 20 feet tall and its shadow is 15 feet long, so the ratio is .

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

3. Cross - multiply to solve for . We get

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