Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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).](https://content.bartleby.com/qna-images/question/2f3e5dad-3eef-4af4-8432-92621aeb9e2a/589a7236-9c61-4d86-ad5d-6cb0f82be15b/ovomemn_processed.jpeg)
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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