To solve for the height at which the top of the ladder touches the house, we can model the scenario using a right triangle. Here, the ladder represents the hypotenuse, the distance from the bottom of the ladder to the base of the house represents one leg, and the height at which the ladder contacts the wall represents the other leg.
Given:
- Length of the ladder (hypotenuse) = 20 feet
- Distance from the base of the house (one leg) = 5 feet
Let \( h \) be the height that the ladder reaches on the house. According to the Pythagorean theorem, we have:
\[ \text{(length of ladder)}^2 = \text{(distance from base)^2} + \text{(height)}^2 \]
Substituting the known values:
\[ 20^2 = 5^2 + h^2 \]
Calculating the squares:
\[ 400 = 25 + h^2 \]
Now, we will isolate \( h^2 \):
\[ h^2 = 400 - 25 \] \[ h^2 = 375 \]
Next, we will take the square root of both sides to find \( h \):
\[ h = \sqrt{375} \]
Calculating \( \sqrt{375} \):
\[ h \approx 19.364 \]
Rounding to the nearest tenth of a foot:
\[ h \approx 19.4 \text{ feet} \]
Thus, the height at which the top of the ladder is touching the house is approximately 19.4 feet.