A 10 -ft-tall fence runs parallel to the wall of a house at a distance of $6 \mathrm{ft}$. Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house is $20 \mathrm{ft}$ high and the horizontal ground extends $20 \mathrm{ft}$ from the fence.

Step 1 ：This is a geometry problem. We can solve it by using the Pythagorean theorem. The ladder, the wall of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse of the triangle. The length of the wall of the house is one of the legs of the triangle, and the distance from the base of the ladder to the wall of the house is the other leg of the triangle.

Step 2 ：We can find the length of the ladder by using the Pythagorean theorem: the square of the length of the ladder is equal to the sum of the squares of the lengths of the other two sides.

Step 3 ：Given that the height of the wall is \(20\) feet and the horizontal distance from the fence to the wall is \(20\) feet, and the distance from the fence to the base of the ladder is \(6\) feet, the total distance from the base of the ladder to the wall of the house is \(20 + 6 = 26\) feet.

Step 4 ：By substituting the given values into the Pythagorean theorem, we get \(ladder\_length = \sqrt{height^2 + distance^2} = \sqrt{20^2 + 26^2} = 32.802438933713454\) feet.

Step 5 ：Final Answer: The length of the shortest ladder that extends from the ground to the house without touching the fence is approximately \(\boxed{32.80}\) feet.