Scout places his 20-foot step ladder against a house he is painting. If the bottom of the ladder is 5 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot?(1 point)

To find out how high the top of the ladder is touching the house, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the lengths of the other two sides (the distance from the bottom of the ladder to the house, and the height at which the ladder touches the house).

Let:
- \( a \) = height the ladder reaches on the house (opposite side)
- \( b \) = distance from the house to the bottom of the ladder (adjacent side) = 5 feet
- \( c \) = length of the ladder (hypotenuse) = 20 feet

According to the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Substituting the known values:

\[
20^2 = a^2 + 5^2
\]

Calculating:

\[
400 = a^2 + 25
\]

Now, subtract 25 from both sides:

\[
400 - 25 = a^2
\]
\[
375 = a^2
\]

Now, take the square root of both sides to find \( a \):

\[
a = \sqrt{375} \approx 19.4 \text{ feet}
\]

Therefore, the height above the ground at which the top of the ladder is touching the house is approximately **19.4 feet**.