To find the height at which the ladder reaches the wall, we can use the Pythagorean theorem. Let's denote the following:
- The length of the ladder \( L = 12 \) feet (this is the hypotenuse).
- The distance from the wall \( d = 5 \) feet (this is one leg of the right triangle).
- The height of the ladder on the wall \( h \) (this is the other leg of the right triangle, which we want to find).
According to the Pythagorean theorem:
\[ L^2 = d^2 + h^2 \]
Substituting the known values:
\[ 12^2 = 5^2 + h^2 \]
Calculating the squares:
\[ 144 = 25 + h^2 \]
Now, isolate \( h^2 \):
\[ h^2 = 144 - 25 \] \[ h^2 = 119 \]
Now, take the square root to find \( h \):
\[ h = \sqrt{119} \]
Calculating \( \sqrt{119} \):
\[ h \approx 10.9087 \]
Rounding to the nearest tenth, we find:
\[ h \approx 10.9 \text{ feet} \]
Thus, the distance from the ground that the ladder reaches the wall is approximately 10.9 feet.