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)

13.4 ft

10.4 ft

180 ft

108 ft

Answer 1

To solve the problem, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case:
- The ladder acts as the hypotenuse (12 ft).
- The distance from the base of the house to the bottom of the ladder is one leg (6 ft).
- The height that the ladder reaches on the house is the other leg, which we need to find.

Let \( h \) be the height that the ladder reaches. According to the Pythagorean Theorem:

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

Calculating the squares:

\[
h^2 + 36 = 144
\]

Now we will isolate \( h^2 \):

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

Now, take the square root of both sides to find \( h \):

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

Rounding to the nearest tenth:

\[
h \approx 10.4
\]

Thus, the height that the ladder will reach is **10.4 ft**.