a. A wheelchair ramp with a length of 113 inches has a horizontal distance of 112 inches. What is the​ ramp's vertical​ distance?
b. Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 inch requires a horizontal run of 12 inches. Does this ramp satisfy the​ requirements? 
 The vertical distance of the ramp is 


To solve these problems, let's break them down:

### Part (a): Finding the Vertical Distance

We are given:
- The length of the ramp (the hypotenuse) is \(113\) inches.
- The horizontal distance (the base of the right triangle) is \(112\) inches.

Using the Pythagorean theorem:

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

Where:
- \(a\) is the vertical distance we need to find,
- \(b = 112\) inches is the horizontal distance,
- \(c = 113\) inches is the length of the ramp.

Now, solve for \(a\):

\[
a^2 = c^2 - b^2 = 113^2 - 112^2
\]
\[
a^2 = 12769 - 12544 = 225
\]
\[
a = \sqrt{225} = 15 \, \text{inches}
\]

Thus, the vertical distance of the ramp is **15 inches**.

---

### Part (b): Checking if the Ramp Satisfies the Requirements

The law requires that for every vertical rise of 1 inch, there must be a horizontal run of 12 inches. So, let's check the ratio for the given ramp.

The vertical rise is \(15\) inches, and the horizontal run is \(112\) inches.

The required horizontal run for \(15\) inches of vertical rise would be:

\[
\text{Required horizontal run} = 15 \times 12 = 180 \, \text{inches}
\]

Since the actual horizontal run is only \(112\) inches, the ramp does **not** meet the legal requirements.

---

Let me know if you'd like further details or explanations!

---

Here are five related questions:
1. How would the vertical distance change if the ramp length increased to 120 inches?
2. How can you calculate the slope of the ramp using trigonometry?
3. What modifications would need to be made to this ramp to satisfy legal requirements?
4. How do different types of triangles affect the application of the Pythagorean theorem?
5. What are the consequences of non-compliance with construction laws for access ramps?

**Tip:** Always double-check the ratios and legal requirements in construction projects to ensure safety and compliance.

a. A wheelchair ramp with a length of 113 inches has a horizontal distance of 112 inches. What is the ramp's vertical distance? b. Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 inch requires a horizontal run of 12 inches. Does this ramp satisfy the requirements?

Learn how to calculate the vertical distance of a 113-inch wheelchair ramp using the Pythagorean Theorem, and check if the ramp meets construction law requirements. The solution involves geometric concepts and ratio checks to ensure compliance for disabled access. Suitable for students in Grades 8-10.

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