Question

As a reminder the requirement for a ramp to be ADA compliant is that it must be first no more than 30 inches tall and it must have a slope of no larger than 1/12 in rise to run or in other words no greater angle of elevation than 4.76°. Would a ramp that rises 20 inches and has a horizontal run of 70 inches be ADA compliant? Show both via slope (rise/run) and via the angle of elevation. 4pts. total: 2pts slope with work. 2pts angle with work Include whether ADA compliant or not with reasoning You may upload an image of your answer and work if you prefer.

Answer 1

To determine if the ramp is ADA compliant, we need to check both the slope (rise/run) and the angle of elevation.

### **Slope Calculation**
1. **Identify the rise and run:**
- Rise (vertical height) = 20 inches
- Run (horizontal distance) = 70 inches

2. **Calculate the slope (rise/run):**
\[
\text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{20 \text{ inches}}{70 \text{ inches}}
\]
\[
\text{Slope} = \frac{20}{70} = \frac{2}{7} \approx 0.2857
\]

3. **Check for ADA compliance:**
The ADA standard states that the slope should be 1:12, which can also be expressed as:
\[
\text{Slope} \leq \frac{1 \text{ inch}}{12 \text{ inches}} \approx 0.0833
\]

Since \(0.2857\) is greater than \(0.0833\), the slope does not meet the ADA requirement.

### **Angle of Elevation Calculation**
1. **Calculate the angle (θ) using the tangent function:**
\[
\tan(\theta) = \frac{\text{Rise}}{\text{Run}} = \frac{20}{70} = \frac{2}{7} \approx 0.2857
\]

2. **Determine the angle using the inverse tangent function:**
\[
\theta = \tan^{-1}(0.2857) \approx 15.9°
\]

3. **Check for ADA compliance:**
The maximum angle allowed by ADA is 4.76°. Since 15.9° is significantly greater than 4.76°, this further confirms that the ramp is not ADA compliant.

### **Conclusion**
- **Slope:** \(0.2857\) (greater than ADA maximum of \(0.0833\)) → **Not compliant.**
- **Angle:** \(15.9°\) (greater than ADA maximum of \(4.76°\)) → **Not compliant.**

Thus, the ramp that rises 20 inches with a horizontal run of 70 inches is **NOT ADA compliant** due to both slope and angle considerations.