9. Wheelchair ramps must have an angle of elevation no more than 4.8°. The wheelchair ramp outside of a local boutique has a slope of 3.5/5. Is the ramp ADA complaint? Draw a picture and show all work.

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### Understanding Wheelchair Ramps and Compliance with ADA Standards

**Question 9:**  
Wheelchair ramps must have an angle of elevation no more than 4.8°. The wheelchair ramp outside of a local boutique has a slope of 3.5/5. Is the ramp ADA compliant? Draw a picture and show all work.

---

**Discussion:**

To determine whether the wheelchair ramp is ADA compliant, we need to compare the given slope with the maximum allowable angle of elevation of 4.8°.

**Step-by-step Solution:**

1. **Convert the Slope to Angle of Elevation:**

   The slope given is \(\frac{3.5}{5}\).
   - The slope (m) can be converted into an angle (θ) using the arctangent function: \(\theta = \arctan(m)\).
   - Calculating \(\theta:\):
   \[
   \theta = \arctan\left(\frac{3.5}{5}\right)
   \]
   
   Using a calculator to find the angle:
   \[
   \theta \approx \arctan(0.7) \approx 35°
   \]

2. **Compare with ADA Standards:**
   - The maximum allowable angle of elevation is 4.8°.
   - The calculated angle of \( \approx 35° \) is significantly greater than 4.8°.

**Conclusion:**

The wheelchair ramp with a slope of \(\frac{3.5}{5}\) is not ADA compliant as its angle of elevation exceeds the maximum allowable 4.8°.

**Visual Representation:**

To visually illustrate the problem, draw a right triangle where:
- The horizontal side (base) represents 5 units.
- The vertical side (rise) represents 3.5 units.

Label the angle of elevation (θ) and the corresponding slope ratio (3.5/5).

```plaintext
                3.5 (rise)
                 |
                 | 
                 |θ
                 |   
-----------------|
      5 (run)
```

This visual shows that the rise over the run produces a steeper incline than allowed by ADA standards (southwestern style of representation for better understanding).
Transcribed Image Text:### Understanding Wheelchair Ramps and Compliance with ADA Standards **Question 9:** Wheelchair ramps must have an angle of elevation no more than 4.8°. The wheelchair ramp outside of a local boutique has a slope of 3.5/5. Is the ramp ADA compliant? Draw a picture and show all work. --- **Discussion:** To determine whether the wheelchair ramp is ADA compliant, we need to compare the given slope with the maximum allowable angle of elevation of 4.8°. **Step-by-step Solution:** 1. **Convert the Slope to Angle of Elevation:** The slope given is \(\frac{3.5}{5}\). - The slope (m) can be converted into an angle (θ) using the arctangent function: \(\theta = \arctan(m)\). - Calculating \(\theta:\): \[ \theta = \arctan\left(\frac{3.5}{5}\right) \] Using a calculator to find the angle: \[ \theta \approx \arctan(0.7) \approx 35° \] 2. **Compare with ADA Standards:** - The maximum allowable angle of elevation is 4.8°. - The calculated angle of \( \approx 35° \) is significantly greater than 4.8°. **Conclusion:** The wheelchair ramp with a slope of \(\frac{3.5}{5}\) is not ADA compliant as its angle of elevation exceeds the maximum allowable 4.8°. **Visual Representation:** To visually illustrate the problem, draw a right triangle where: - The horizontal side (base) represents 5 units. - The vertical side (rise) represents 3.5 units. Label the angle of elevation (θ) and the corresponding slope ratio (3.5/5). ```plaintext 3.5 (rise) | | |θ | -----------------| 5 (run) ``` This visual shows that the rise over the run produces a steeper incline than allowed by ADA standards (southwestern style of representation for better understanding).
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