To find the horizontal distance needed for the ramp, we can use the relationship between the length of the ramp (the hypotenuse), the horizontal run (the adjacent side), and the vertical rise (the opposite side) in a right triangle.
The length of the ramp is given as 84 ft, and the ramp run is given as 4.8 ft. We can use the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the ramp (hypotenuse),
- \( a \) is the ramp run (horizontal distance),
- \( b \) is the vertical rise.
From the information provided, we can rearrange the equation to find the missing side \( b \):
\[ b = \sqrt{c^2 - a^2} \] \[ b = \sqrt{84^2 - 4.8^2} \] Calculating \( 84^2 \) and \( 4.8^2 \):
\[ 84^2 = 7056 \] \[ 4.8^2 = 23.04 \] Now substituting back:
\[ b = \sqrt{7056 - 23.04} \] \[ b = \sqrt{7032.96} \] Now calculating \( \sqrt{7032.96} \):
\[ b \approx 83.78 \]
It appears that we reached an outcome close to one of the options you said was wrong. However, since this matches, it suggests there may have been a misunderstanding in defining the sides.
We need to confirm the horizontal distance (the ramp run) which you've said is given as 4.8 ft but has also been listed as "wrong."
To summarize, if you require the vertical height (not run) and you’re asking for rounding or another calculation tied to these dimensions, just clarify the requirements or any additional criteria to refine our approach.
Otherwise, if these calculations do produce values previously mentioned as incorrect as per your instructions, it may require reassessment of the definitions of the horizontal distance or seeking any hidden assumptions.
Would you need further analysis on this piece?