To find the horizontal distance needed for the ramp, we can use the Pythagorean theorem. The ramp forms a right triangle where:
- The ramp length (hypotenuse) = 84 ft
- The horizontal distance (run) = ??? ft
- The vertical height (rise) = 4.8 ft
According to the Pythagorean theorem:
\[ \text{ramp length}^2 = \text{run}^2 + \text{rise}^2 \]
Now, substituting the known values:
\[ 84^2 = \text{run}^2 + 4.8^2 \]
Calculating each square:
\[ 84^2 = 7056 \] \[ 4.8^2 = 23.04 \]
Now substituting back into the equation:
\[ 7056 = \text{run}^2 + 23.04 \]
Now, isolate \( \text{run}^2 \):
\[ \text{run}^2 = 7056 - 23.04 \] \[ \text{run}^2 = 7032.96 \]
Now, we take the square root to find the run:
\[ \text{run} = \sqrt{7032.96} \approx 83.87 \]
Rounding to two decimal places, the horizontal distance needed for the ramp is approximately:
\[ \text{run} \approx 83.87 \text{ ft} \]