To determine how high the window is from the ground, we can use the Pythagorean theorem. The ladder, the distance from the base of the ladder to the house, and the height of the window form a right triangle.
Let's denote:
- The length of the ladder as \( c = 12 \) feet (the hypotenuse).
- The distance from the base of the ladder to the house as \( a = 6 \) feet (one leg).
- The height of the window as \( b \) (the other leg), which we want to find.
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting the known values:
\[ 6^2 + b^2 = 12^2 \]
Calculating the squares:
\[ 36 + b^2 = 144 \]
Subtracting 36 from both sides gives:
\[ b^2 = 144 - 36 \]
\[ b^2 = 108 \]
To find \( b \), we take the square root:
\[ b = \sqrt{108} \approx 10.39 \]
Therefore, the height of the window from the ground is approximately 10.39 feet.
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