Question

Use the Pythagorean Theorem Quick Check
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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

180 ft.
180 ft.

10.4 ft.
10.4 ft.

13.4 ft.
13.4 ft.

108 ft.

Answer 1

To find out how high the ladder will reach using the Pythagorean Theorem, you can use the formula:

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

where:
- \( a \) is the height the ladder reaches,
- \( b \) is the distance from the base of the house to the bottom of the ladder (6 ft), and
- \( c \) is the length of the ladder (12 ft).

Plugging in the values:
\[
a^2 + 6^2 = 12^2
\]

This simplifies to:
\[
a^2 + 36 = 144
\]

Next, subtract 36 from both sides:
\[
a^2 = 144 - 36
\]
\[
a^2 = 108
\]

Now, take the square root of both sides to find \( a \):
\[
a = \sqrt{108} \approx 10.39
\]

Rounding to the nearest tenth, \( a \approx 10.4 \) ft.

So, the correct answer is **10.4 ft.**