A wheelchair ramp has an angle of 6 degrees,side length 29ft and height 3ft.
For a safe ramp,the ratio of vertical distance: horizontal distance needs to be less than 1:12. Would the ramp be considered a safe ramp?
Please show me how to do this! Thank you
safe ramp:
tanØ = 1/12
Ø = 4.76°
Since your angle is greater than that, it is not safe
To determine whether the ramp is considered safe, we need to calculate the ratio of the vertical distance to the horizontal distance and compare it with the given standard of 1:12.
The vertical distance is the height of the ramp, which is given as 3ft, and the horizontal distance is the length of the ramp, given as 29ft.
To find the ratio, we divide the vertical distance by the horizontal distance:
Ratio = Vertical distance / Horizontal distance
Ratio = 3ft / 29ft
To determine if this ratio is less than 1:12, compare it to the standard:
Ratio < 1:12
To compare the ratio with 1:12, we can convert 1:12 into the same units as our ratio, which is feet:
1:12 = 1ft / 12ft
Now, we can compare the two ratios:
Ratio = 3ft / 29ft
1:12 = 1ft / 12ft
To compare these ratios, we need to find a common denominator. In this case, the least common denominator is 348ft (29ft * 12ft).
Ratio = (3ft * 12ft) / (29ft * 12ft)
1:12 = 1ft / 12ft
Ratio = 36ft / 348ft
1:12 = 29ft / 348ft
Now we can compare the two ratios:
Ratio < 1:12
36ft / 348ft < 29ft / 348ft
Canceling out the common denominator, we have:
36ft < 29ft
Since 36ft is greater than 29ft, the ratio of the vertical distance to the horizontal distance is not less than the 1:12 standard. Therefore, the ramp is not considered safe.
In conclusion, the given wheelchair ramp with an angle of 6 degrees, a length of 29ft, and a height of 3ft is not considered safe according to the 1:12 ratio requirement.