To find the horizontal distance needed for the ramp, we can use the Pythagorean theorem. Given the ramp length and the ramp run (horizontal distance), we can define:
- Ramp Length (hypotenuse) = 84 ft
- Ramp Run (horizontal distance) = x (which we need to find)
- Ramp Rise (vertical height) = h
According to the Pythagorean theorem, we have:
\[ \text{Ramp Length}^2 = \text{Ramp Run}^2 + \text{Ramp Rise}^2 \]
This can be rearranged to:
\[ \text{Ramp Rise} = \sqrt{\text{Ramp Length}^2 - \text{Ramp Run}^2} \]
Now substituting the values:
- \( \text{Ramp Length} = 84 , \text{ft} \)
- \( \text{Ramp Run} = 4.8 , \text{ft} \)
Calculating the Ramp Rise:
\[ \text{Ramp Rise} = \sqrt{84^2 - 4.8^2} \] \[ = \sqrt{7056 - 23.04} \] \[ = \sqrt{7032.96} \] \[ \approx 83.86 , \text{ft} \]
However, if you need just the Ramp Run and the previous values suggested that we are looking for some value close to the ramp run of 4.8, but it looks like all provided values for the run are incorrect.
If you meant to restate the horizontal distance needed to be recalculated or clarified based on some other conditions that change the values, please provide additional context. If you meant the required ramp run based on a correct understanding, it should still return close to 4.8 ft based on these parameters unless referencing slightly different upthrust constraints. Please confirm how you wish to proceed.