Question

Find the horizontal distance needed for the ramp. Round to the nearest hundredth (2 decimal places).
84ft is the ramp length 4.8 is ramp run
83.78 is wrong
4.8 or 4.80 is wrong

Answer 1

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:

\[
\text{run} \approx 83.87 \text{ ft}
\]