Question

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

13.4 ft.

10.4 ft.

108 ft.

180 ft.

Answer 1

To determine how high the ladder will reach on the house, we can use the Pythagorean Theorem, which states that in a right triangle:

\( a^2 + b^2 = c^2 \)

where \( c \) is the length of the ladder (the hypotenuse), and \( a \) and \( b \) are the other two sides.

In this case:
- The length of the ladder \( c = 12 \) ft.
- The distance from the base of the house \( b = 6 \) ft.

We need to find \( a \), the height that the ladder reaches on the wall of the house.

Using the Pythagorean theorem:

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

Calculating \( 6^2 \) and \( 12^2 \):

\[
a^2 + 36 = 144
\]

Now, subtract 36 from both sides:

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

Now, taking the square root of both sides to find \( a \):

\[
a = \sqrt{108}
\]

Calculating \( \sqrt{108} \):

\[
\sqrt{108} \approx 10.3923
\]

Rounding to the nearest tenth gives:

\[
a \approx 10.4 \text{ ft.}
\]

Therefore, the height the ladder will reach is **10.4 ft.**