To solve this problem using the Pythagorean theorem, we can set up the equation based on the relationship between the height of the ladder on the wall (let's call it \( h \)), the distance from the bottom of the ladder to the base of the house (which is 6 ft), and the length of the ladder (which is 12 ft).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is the height the ladder reaches on the wall (which is \( h \)),
- \( b \) is the distance from the base of the house to the bottom of the ladder (which is 6 ft),
- \( c \) is the length of the ladder (which is 12 ft).
Substituting these values in, we have:
\[ h^2 + 6^2 = 12^2 \]
Now we calculate \( 6^2 \) and \( 12^2 \):
\[ h^2 + 36 = 144 \]
Next, subtract 36 from both sides:
\[ h^2 = 144 - 36 \] \[ h^2 = 108 \]
Now, take the square root of both sides to find \( h \):
\[ h = \sqrt{108} \]
Calculating the square root of 108:
\[ h \approx 10.39 \]
Rounding to the nearest tenth, the height the ladder will reach is approximately:
\[ \boxed{10.4} \text{ ft} \]
1 answer