To find the length of the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
- The height of the ramp (one side) is 6 feet.
- The horizontal distance from the base of the ramp to the truck (the other side) is 8 feet.
We denote the length of the ramp (the hypotenuse) as \( c \).
According to the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where \( a \) is the height (6 feet) and \( b \) is the horizontal distance (8 feet).
Substituting in the values:
\[ c^2 = 6^2 + 8^2 \] \[ c^2 = 36 + 64 \] \[ c^2 = 100 \]
Now, to find \( c \), we take the square root of both sides:
\[ c = \sqrt{100} = 10 \]
Thus, the length of the ramp is:
\[ \boxed{10} \text{ feet} \]
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