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This problem involves finding the horizontal distance from the base of the escalator to the point on the first floor directly below the top of the escalator, forming a right triangle with the length of the escalator and the height between the floors. We can apply the Pythagorean theorem to solve this.

In the given scenario:
- The length of the escalator is the hypotenuse of the triangle (30 feet).
- The height between the floors is one leg of the triangle (12 feet).
- We need to find the length of the other leg (the horizontal distance from the base to the point directly below the top of the escalator).

Using the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Where:
- \(c\) is the hypotenuse (30 feet),
- \(a\) is the height (12 feet),
- \(b\) is the horizontal distance, which we need to find.

Substituting the known values:

\[
30^2 = 12^2 + b^2
\]

\[
900 = 144 + b^2
\]

Now, subtract 144 from both sides:

\[
756 = b^2
\]

Taking the square root of both sides:

\[
b = \sqrt{756} \approx 27.5 \text{ feet}
\]

So, the horizontal distance is approximately 27.5 feet, which corresponds to option **D**.

Let me know if you need further details or have other questions! Here are a few related questions:

1. How does the Pythagorean theorem apply to different geometric shapes?
2. Can you solve for a missing side if only the other two sides of a triangle are known?
3. What is the significance of the Pythagorean theorem in real-world applications?
4. How would this problem change if the escalator was placed at an angle other than 90 degrees?
5. What other methods could you use to solve this problem?

**Tip**: Remember that the Pythagorean theorem only works for right-angled triangles!

An escalator runs from the first floor of a shopping mall to the second floor. The length of the escalator is 30 feet, and the distance between the floors is 12 feet. Find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator. Round your answer to the nearest tenth if necessary.

Learn how to solve a right triangle problem involving an escalator in a shopping mall using the Pythagorean theorem. With a hypotenuse of 30 feet and a height of 12 feet, find the horizontal distance to the nearest tenth. Suitable for Grades 7-9.

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