3. A wheelchair ramp is to be rated at 8%, which means that it rises 8 cm for every 100 cm of horizontal distance. The height of the ramp is 35 cm.
A.What is the length of this ramp?
B.What is the angle this ramp makes with the horizontal?
C.To what minimum length should the ramp be extended to meet government regulations of a maximum 3% incline?
A. To find the length of the ramp, we can use the formula: length = height/rise * 100. Given that the rise is 8 cm for every 100 cm of horizontal distance, we can substitute the values into the formula:
length = 35 cm / 8 cm * 100 = 437.5 cm
Therefore, the length of the ramp is 437.5 cm.
B. To find the angle the ramp makes with the horizontal, we can use the inverse tangent function (tan^-1). The formula is:
angle = tan^-1(rise/length) * 180/π
Substituting the values into the formula:
angle = tan^-1(8/437.5) * 180/π = 1.03 degrees
Therefore, the angle this ramp makes with the horizontal is approximately 1.03 degrees.
C. To find the minimum length the ramp should be extended to meet government regulations of a maximum 3% incline, we can use the formula: length = height/rise * 100. Given that the rise should now be 3 cm for every 100 cm of horizontal distance, we can substitute the values into the formula:
length = 35 cm / 3 cm * 100 = 1166.67 cm
Therefore, the minimum length the ramp should be extended to meet government regulations is approximately 1166.67 cm.
To find the answers to these questions, we can use trigonometry and proportional reasoning.
A. To find the length of the ramp, we can use the ratio of rise to horizontal distance. Since the ramp has a rise of 8 cm for every 100 cm of horizontal distance, we can set up the following proportion:
8 cm / 100 cm = 35 cm / x
To solve for x, we can cross-multiply and divide:
8 cm * x = 35 cm * 100 cm
x = (35 cm * 100 cm) / 8 cm
Simplifying the equation:
x = 437.5 cm
Therefore, the length of the ramp is 437.5 cm.
B. To find the angle the ramp makes with the horizontal, we can use trigonometry. The tangent of an angle is equal to the rise divided by the run (horizontal distance).
tan(angle) = rise / run
In this case, the rise is 35 cm and the run is 437.5 cm.
tan(angle) = 35 cm / 437.5 cm
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(35 cm / 437.5 cm)
Using a calculator, we find that the angle is approximately 4.59 degrees.
Therefore, the ramp makes an angle of approximately 4.59 degrees with the horizontal.
C. To find the minimum length the ramp should be extended to meet government regulations of a maximum 3% incline, we can use the same method as in part A. We need to find the length when the rise is 3% of the horizontal distance.
3% of the horizontal distance = (3/100) * x
We can set up the following proportion:
8 cm / 100 cm = (3/100) * x / x
To solve for x, we can cross-multiply and divide:
8 cm * x = (3/100) * x * 100 cm
Simplifying the equation:
8 cm * x = 3 cm * x
8 cm = 3 cm * x / x
Simplifying further:
8 cm = 3 cm
Since the equation simplifies to 8 cm = 3 cm, it means that there is no solution. This implies that the ramp cannot be extended to meet the government regulations of a maximum 3% incline with the given height of 35 cm.
Therefore, there is no minimum length for the ramp to meet the government regulations of a maximum 3% incline.