To find the ramp length needed, we will use the Pythagorean theorem. In this context, the height of the ramp (5 ft) and the length of the ramp (4.8 ft) represent the two legs of a right triangle, and the ramp length itself is the hypotenuse.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \(c\) is the hypotenuse (the ramp length),
- \(a\) is the height (5 ft),
- \(b\) is the length (4.8 ft).
Substituting in the values:
\[ c^2 = 5^2 + 4.8^2 \]
Calculating \(5^2\) and \(4.8^2\):
\[ 5^2 = 25 \ 4.8^2 = 23.04 \]
Now, add those together:
\[ c^2 = 25 + 23.04 = 48.04 \]
To find \(c\), take the square root:
\[ c = \sqrt{48.04} \approx 6.93 \]
Therefore, the ramp length needed, rounded to the nearest hundredth, is approximately 6.93 ft.