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To solve the problem, we can use the principle of similar triangles. Both the radio tower and the yardstick form similar triangles with their shadows. This means the ratios of their heights to the lengths of their shadows are equal.

Given:
- Shadow of the radio tower = 8 feet
- Height of the yardstick = 1 yard = 3 feet
- Shadow of the yardstick = 0.5 inches = \(\frac{1}{24}\) feet

Let \(h\) be the height of the radio tower. We can set up the following proportion:

\[
\frac{h}{8} = \frac{3}{\frac{1}{24}}
\]

First, convert \(\frac{1}{24}\) feet to a single fraction:

\[
\frac{3}{\frac{1}{24}} = 3 \times 24 = 72
\]

So the proportion becomes:

\[
\frac{h}{8} = 72
\]

Solving for \(h\):

\[
h = 72 \times 8 = 576 \text{ feet}
\]

Therefore, the height of the radio tower is 576 feet.

Would you like more details or have any questions? Here are 5 questions you might want to ask next:

1. How do you determine the proportionality in similar triangles?
2. What are other real-life applications of similar triangles?
3. Can you explain more about unit conversions in this problem?
4. What if the height of the yardstick was different? How would that affect the solution?
5. How can I verify the solution using a different method?

**Tip:** When dealing with similar triangles, always ensure the units of measurement are consistent before setting up the proportion.

Discover how to determine the height of a radio tower using the principle of similar triangles. This problem involves calculating the height of the tower based on its shadow and comparing it to the height of a yardstick. Suitable for advanced high school students.

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