A hospital plans to build a wheelchair ramp. It's slope must be less than 1/12 . The entrance to the hospital is 70cm above the ground. What is the minimum horizontal distance needed for the ramp?
Well, to calculate the minimum horizontal distance needed for the ramp, we need to think outside the box. Or in this case, outside the slope.
Now, we know that the slope must be less than 1/12, which means that for every 12 units of horizontal distance, the ramp can only increase by 1 unit vertically.
To find the minimum horizontal distance, we can set up a ratio. Let's call the horizontal distance "x" (in centimeters).
So, the ratio between the vertical increase (70cm) and the horizontal distance (x) should be less than 1/12:
70cm / x < 1/12
To get rid of the pesky fraction, we can multiply both sides of the inequality by 12:
12 * (70cm / x) < 1
Now, let's do some math:
840cm / x < 1
To find the minimum horizontal distance, we want to isolate "x". Let's multiply both sides of the inequality by "x":
840cm < x
So, the minimum horizontal distance needed for the ramp is 840 centimeters or 8.4 meters. That's a pretty long ramp, but hey, at least you'll have plenty of room to practice your wheelchair tricks!
To find the minimum horizontal distance needed for the ramp, we can use the formula:
Horizontal Distance = Tan(Angle) x Vertical Distance
Here, the angle is determined by the slope, which must be less than 1/12. We can convert this to its decimal equivalent by dividing 1 by 12:
1/12 = 0.0833
So, the maximum slope we can have for the ramp is 0.0833. To find the angle, we can take the inverse tangent (tan^-1) of this value:
Angle = tan^-1(0.0833)
Using a calculator, we find that the angle is approximately 4.76 degrees.
The vertical distance is given as 70 cm. So, to find the horizontal distance, we substitute the values into the formula:
Horizontal Distance = Tan(4.76 degrees) x 70 cm
Again, using a calculator, we find that Tan(4.76 degrees) is approximately 0.0832.
Therefore,
Horizontal Distance ≈ 0.0832 x 70 cm
Horizontal Distance ≈ 5.824 cm
Thus, the minimum horizontal distance needed for the ramp is approximately 5.824 cm.
Thanks!
70/x < 1/12
x > 840 cm