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)

Question

180 ft.
• 10.4 ft.
13.4 ft.
• 108 ft.

Answer 1

To find how high the ladder will reach, we can use the Pythagorean Theorem, which states:

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

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).

We can substitute the values we have into the equation:

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

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

\[ a^2 + 36 = 144 \]

Now, subtract 36 from both sides to solve for \( a^2 \):

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

Next, we take the square root of both sides to find \( a \):

\[ a = \sqrt{108} \]

Calculating \( \sqrt{108} \):

\[ a \approx 10.3923 \]

Rounding to the nearest tenth, we get:

\[ a \approx 10.4 \]

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