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.
13.4 ft.

10.4 ft.
10.4 ft.

108 ft.
108 ft.

180 ft.

Answer 1

To find out how high the ladder reaches against the house, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder in this case) is equal to the sum of the squares of the lengths of the other two sides.

In this scenario:
- The length of the ladder (hypotenuse) is 12 ft.
- The distance from the base of the ladder to the house (one leg of the triangle) is 6 ft.
- We need to find the height (the other leg of the triangle).

Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) is the height we are looking for,
- \(b\) is the distance from the base of the ladder to the house (6 ft),
- \(c\) is the length of the ladder (12 ft).

Substituting the known values:
\[
a^2 + 6^2 = 12^2
\]
\[
a^2 + 36 = 144
\]
Now, subtract 36 from both sides:
\[
a^2 = 144 - 36
\]
\[
a^2 = 108
\]
Now, take the square root of both sides:
\[
a = \sqrt{108} \approx 10.4 \text{ ft}
\]

So the height the ladder will reach is approximately 10.4 ft.

The correct answer is:
**10.4 ft.**