Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?(1 point) Responses 10.4 ft. 10.4 ft. 180 ft. 180 ft. 108 ft. 108 ft. 13.4 ft.

To find out how high the ladder reaches, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

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

In this scenario:

• The hypotenuse (c) is the length of the ladder, which is 12 ft.
• One leg (a) is the height we want to find, and the other leg (b) is the distance from the house, which is 6 ft.

Plugging in the values we have:

\[ 12^2 = a^2 + 6^2 \] \[ 144 = a^2 + 36 \]

Now, subtract 36 from both sides:

\[ 144 - 36 = a^2 \] \[ 108 = a^2 \]

Next, take the square root of both sides to find a:

\[ a = \sqrt{108} \]

Calculating that gives:

\[ a \approx 10.39 \]

Rounding to the nearest tenth, we find:

\[ a \approx 10.4 \]

Thus, the height the ladder reaches is approximately 10.4 ft.