ramp needs an angle of elevation no greater than 4.8. the business has 8 ft to build the ramp. the ramp must rise 6 inches above the ground. can a ramp be built in this space? if a ramp can be built what is the minimum horizontal distance possible?
please show work. i'm totally lost.
let the rise be x ft, then , 1/2 < x < 8
the run will be 8-x ft
slope of ramp ≤ tan 4.8° or slope ≤ .08397...
slope = x/(8-x) ≤ .08397..
x ≤ .671778... - .08397x
1.08397.. x ≤ .671778..
x ≤ .6197 ft
So the rise has to be from .5 ft to .6197 ft
and the length would be from 7.5 ft to 7.38 ft
Finish answering the question.
To determine whether a ramp can be built within the given space and the minimum horizontal distance possible, we need to use some trigonometry.
Let's start by converting the measurements to the same unit:
- The 8 ft available to build the ramp is equivalent to 8 * 12 = 96 inches.
- The 6-inch rise is already in inches.
Next, we need to determine the length of the ramp, which is the hypotenuse of the right triangle. The vertical distance is the rise of the ramp, and the horizontal distance is what we're trying to find. We can use the tangent function to calculate the angle of elevation:
tan(angle) = rise / run
Substituting the given values:
tan(angle) = 6 inches / horizontal distance
To find the minimum horizontal distance possible, we need to find the minimum angle of elevation we can use. We can rearrange the equation to solve for the horizontal distance:
horizontal distance = rise / tan(angle)
Given that the angle of elevation should not be greater than 4.8, we can substitute this angle into the equation:
horizontal distance = 6 inches / tan(4.8°)
Now, we can calculate the minimum horizontal distance:
horizontal distance = 6 inches / tan(4.8°)
horizontal distance ≈ 6 inches / 0.08323
horizontal distance ≈ 72.09 inches
Therefore, a ramp can be built within the given space, and the minimum horizontal distance possible is approximately 72.09 inches.