To find out how high the ladder will reach on the house using the Pythagorean Theorem, we can represent the situation as a right triangle, where:
- The length of the ladder (hypotenuse) is 12 ft.
- The distance from the base of the house to the bottom of the ladder (one leg) is 6 ft.
- The height the ladder reaches on the house (the other leg) is what we need to find.
The Pythagorean Theorem states that:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
Let:
- \(a = 6\) ft (the distance from the wall)
- \(b\) = height we need to find
- \(c = 12\) ft (the length of the ladder)
Plugging the values into the equation:
\[ 6^2 + b^2 = 12^2 \] \[ 36 + b^2 = 144 \] \[ b^2 = 144 - 36 \] \[ b^2 = 108 \] \[ b = \sqrt{108} \] \[ b \approx 10.4 \text{ ft (when rounded to the nearest tenth)} \]
Thus, the height the ladder will reach is approximately 10.4 ft.
The correct answer is 10.4 ft.