To find the length of the ramp using the Pythagorean theorem, we can represent the ramp as the hypotenuse of a right triangle, where one leg is the height of the ramp (6 feet) and the other leg is the horizontal distance (8 feet).
The Pythagorean theorem states that:
\[ a^2 + b^2 = c^2 \]
where \(a\) and \(b\) are the lengths of the legs of the triangle, and \(c\) is the length of the hypotenuse (the ramp in this case).
In this scenario:
- \(a = 6\) feet (the height)
- \(b = 8\) feet (the horizontal distance)
- \(c\) is what we want to find (the length of the ramp)
Now substituting the values into the equation:
\[ 6^2 + 8^2 = c^2 \] \[ 36 + 64 = c^2 \] \[ 100 = c^2 \]
To find \(c\), we take the square root of both sides:
\[ c = \sqrt{100} \] \[ c = 10 \text{ feet} \]
Thus, the length of the ramp is 10 feet.