In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more tha A builder needs to install a ramp to reach a door that is 2.75 feet off the ground. Is 30 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have? A 30-foot ramp will have an angle of elevation of approximately
In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more tha A builder needs to install a ramp to reach a door that is 2.75 feet off the ground. Is 30 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have? A 30-foot ramp will have an angle of elevation of approximately
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![**Wheelchair Ramp Requirements - ADA Compliance**
To meet the ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8°. In this scenario, a builder needs to install a ramp to reach a door that is 2.75 feet off the ground.
**Problem Statement**
Is a 30-foot long ramp adequate for the straight-line distance to meet these requirements? And what will be the angle of elevation of such a ramp?
### Calculation of the Angle of Elevation
1. **Given Data:**
- Height to be reached (opposite side of the right triangle): 2.75 feet
- Length of the ramp (hypotenuse of the right triangle): 30 feet
2. **Formula Used:**
The angle of elevation \(\theta\) can be calculated using the sine function.
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
\[
\sin(\theta) = \frac{2.75}{30}
\]
\[
\theta = \sin^{-1}\left(\frac{2.75}{30}\right)
\]
3. **Calculation:**
- Divide the opposite side by the hypotenuse:
\[
\frac{2.75}{30} \approx 0.0917
\]
- Find the angle whose sine is 0.0917:
\[
\theta \approx \sin^{-1}(0.0917) \approx 5.26°
\]
### Conclusion
A 30-foot ramp will have an angle of elevation of approximately **5.26°**, which exceeds the ADA maximum requirement of 4.8°. Therefore, a 30-foot ramp is too steep and does not meet the ADA requirement.
**Note:** For compliance, the ramp will need to be longer to reduce the angle of elevation to 4.8° or less.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd39e4536-af56-4cd4-b4a6-67145f8be6a6%2F9a4c6eaa-84f0-4e72-9fc8-989e3ce5d765%2Fh54sael_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Wheelchair Ramp Requirements - ADA Compliance**
To meet the ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8°. In this scenario, a builder needs to install a ramp to reach a door that is 2.75 feet off the ground.
**Problem Statement**
Is a 30-foot long ramp adequate for the straight-line distance to meet these requirements? And what will be the angle of elevation of such a ramp?
### Calculation of the Angle of Elevation
1. **Given Data:**
- Height to be reached (opposite side of the right triangle): 2.75 feet
- Length of the ramp (hypotenuse of the right triangle): 30 feet
2. **Formula Used:**
The angle of elevation \(\theta\) can be calculated using the sine function.
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
\[
\sin(\theta) = \frac{2.75}{30}
\]
\[
\theta = \sin^{-1}\left(\frac{2.75}{30}\right)
\]
3. **Calculation:**
- Divide the opposite side by the hypotenuse:
\[
\frac{2.75}{30} \approx 0.0917
\]
- Find the angle whose sine is 0.0917:
\[
\theta \approx \sin^{-1}(0.0917) \approx 5.26°
\]
### Conclusion
A 30-foot ramp will have an angle of elevation of approximately **5.26°**, which exceeds the ADA maximum requirement of 4.8°. Therefore, a 30-foot ramp is too steep and does not meet the ADA requirement.
**Note:** For compliance, the ramp will need to be longer to reduce the angle of elevation to 4.8° or less.
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