II. Word Problem Reynante Was A Polio Victim And Was Using His Wheelchair For Almost 5 Years Now. One Day, He Visits His Doctor For His Quarterly Check-up And He Passes By The Wheelchair Ramp Which Has A Railing. As Shown In The Illustration At The
II. Word Problem: Reynante's Wheelchair Ramp
Understanding the Problem
Reynante, a polio victim, has been using his wheelchair for almost 5 years. During his quarterly check-up, he passes by a wheelchair ramp with a railing. This scenario presents a real-world problem that requires mathematical analysis. In this article, we will delve into the world of geometry and trigonometry to find the solution to Reynante's problem.
The Problem
The wheelchair ramp has a railing that is 2 meters long and 1 meter high. Reynante wants to know the angle of elevation of the ramp. To find this angle, we need to use trigonometric functions. We will use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.
The Solution
To solve this problem, we need to draw a diagram of the wheelchair ramp and identify the relevant sides of the triangle. Let's call the angle of elevation "θ" (theta). We can see that the opposite side is the height of the railing (1 meter), and the adjacent side is the length of the railing (2 meters).
Using the tangent function, we can write:
tan(θ) = opposite side / adjacent side = 1 meter / 2 meters = 0.5
Finding the Angle
Now that we have the value of the tangent function, we can find the angle of elevation using the inverse tangent function (arctangent). This function returns the angle whose tangent is equal to the given value.
θ = arctan(0.5) = 26.57° (approximately)
Conclusion
Reynante's wheelchair ramp has an angle of elevation of approximately 26.57°. This calculation can be useful in designing wheelchair ramps that are safe and accessible for people with mobility impairments.
Real-World Applications
This problem has real-world applications in various fields, including:
- Architecture: Wheelchair ramps are a crucial feature in building design, especially in public buildings and institutions.
- Engineering: The design of wheelchair ramps requires careful consideration of safety and accessibility.
- Mathematics: Trigonometric functions, such as the tangent function, are essential in solving problems involving right-angled triangles.
Discussion
This problem can be discussed in various categories, including:
- Geometry: The problem involves the use of geometric shapes, such as triangles, to solve a real-world problem.
- Trigonometry: The problem requires the use of trigonometric functions, such as the tangent function, to find the angle of elevation.
- Accessibility: The problem highlights the importance of accessibility in building design, especially for people with mobility impairments.
Additional Problems
Here are some additional problems that can be solved using similar techniques:
- Problem 1: A wheelchair ramp has a railing that is 3 meters long and 1.5 meters high. Find the angle of elevation of the ramp.
- Problem 2: A building has a wheelchair ramp with a railing that is 2 meters long and 1 meter high. Find the angle of elevation of the ramp.
- Problem 3: A person is standing at the bottom of a wheelchair ramp and looking up at the top. The angle of elevation is 30°. Find the height of the ramp.
Solutions
Here are the solutions to the additional problems:
- Problem 1: tan(θ) = 1.5 meters / 3 meters = 0.5. θ = arctan(0.5) = 26.57° (approximately).
- Problem 2: This problem is the same as the original problem, and the solution is θ = 26.57° (approximately).
- Problem 3: tan(θ) = height / 2 meters = 30° / 2 = 15°. θ = arctan(15°) = 1.36 radians (approximately). The height of the ramp is 2 meters * tan(15°) = 0.51 meters (approximately).
Conclusion
In conclusion, Reynante's wheelchair ramp problem is a real-world application of trigonometry and geometry. The solution to this problem can be useful in designing wheelchair ramps that are safe and accessible for people with mobility impairments.
Q&A: Wheelchair Ramp Problems
Frequently Asked Questions
In this article, we will answer some frequently asked questions related to wheelchair ramp problems. These questions cover various aspects of wheelchair ramp design, including safety, accessibility, and mathematics.
Q1: What is the purpose of a wheelchair ramp?
A1: The purpose of a wheelchair ramp is to provide a safe and accessible way for people with mobility impairments to enter and exit buildings. Wheelchair ramps are designed to be gentle and gradual, allowing users to move easily and safely.
Q2: What are the key factors to consider when designing a wheelchair ramp?
A2: When designing a wheelchair ramp, there are several key factors to consider, including:
- Slope: The slope of the ramp should be gentle and gradual, with a maximum slope of 1:12.
- Width: The width of the ramp should be at least 36 inches (91 cm) to accommodate a standard wheelchair.
- Length: The length of the ramp should be sufficient to allow users to move comfortably and safely.
- Handrails: Handrails should be provided on both sides of the ramp to assist users in maintaining balance and stability.
Q3: How do I calculate the angle of elevation of a wheelchair ramp?
A3: To calculate the angle of elevation of a wheelchair ramp, you can use the tangent function. The tangent function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. For example, if the height of the ramp is 1 meter and the length of the ramp is 2 meters, the angle of elevation can be calculated as follows:
tan(θ) = opposite side / adjacent side = 1 meter / 2 meters = 0.5
θ = arctan(0.5) = 26.57° (approximately)
Q4: What is the maximum slope of a wheelchair ramp?
A4: The maximum slope of a wheelchair ramp is 1:12. This means that for every 12 inches (30 cm) of horizontal distance, the ramp should rise by 1 inch (2.5 cm).
Q5: How do I ensure that a wheelchair ramp is safe and accessible?
A5: To ensure that a wheelchair ramp is safe and accessible, you should consider the following factors:
- Slope: The slope of the ramp should be gentle and gradual, with a maximum slope of 1:12.
- Width: The width of the ramp should be at least 36 inches (91 cm) to accommodate a standard wheelchair.
- Length: The length of the ramp should be sufficient to allow users to move comfortably and safely.
- Handrails: Handrails should be provided on both sides of the ramp to assist users in maintaining balance and stability.
- Lighting: The ramp should be well-lit to ensure that users can see the ramp and any obstacles.
- Maintenance: The ramp should be regularly maintained to ensure that it remains safe and accessible.
Q6: Can I use a wheelchair ramp in a residential setting?
A6: Yes, you can use a wheelchair ramp in a residential setting. However, you should ensure that the ramp is designed and installed in accordance with local building codes and regulations.
Q7: How do I calculate the length of a wheelchair ramp?
A7: To calculate the length of a wheelchair ramp, you can use the following formula:
length = height / slope
For example, if the height of the ramp is 1 meter and the slope is 1:12, the length of the ramp can be calculated as follows:
length = 1 meter / (1/12) = 12 meters
Q8: What are the benefits of using a wheelchair ramp?
A8: The benefits of using a wheelchair ramp include:
- Improved accessibility: Wheelchair ramps provide a safe and accessible way for people with mobility impairments to enter and exit buildings.
- Increased independence: Wheelchair ramps allow users to move independently and safely, reducing the need for assistance.
- Reduced risk of injury: Wheelchair ramps reduce the risk of injury by providing a gentle and gradual slope.
Conclusion
In conclusion, wheelchair ramps are an essential feature in building design, especially in public buildings and institutions. By considering the key factors mentioned in this article, you can design and install a wheelchair ramp that is safe, accessible, and compliant with local building codes and regulations.