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

Responses

13.4 ft.
13.4 ft.

108 ft.
108 ft.

10.4 ft.
10.4 ft.

180 ft.

Answer 1

To determine how high the ladder reaches, we can use the Pythagorean Theorem, which is expressed as:

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

where:

• \( c \) is the length of the ladder (the hypotenuse),
• \( a \) is the height reached by the ladder (the vertical side),
• \( b \) is the distance from the base of the ladder to the house (the horizontal side).

In this case:

• \( c = 12 \) ft (the length of the ladder),
• \( b = 6 \) ft (the distance from the house).

We can rearrange the formula to solve for \( a \):

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

Substituting in the values:

\[ a^2 = 12^2 - 6^2 \] \[ a^2 = 144 - 36 \] \[ a^2 = 108 \]

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

\[ a = \sqrt{108} \] \[ a \approx 10.39 \]

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

Thus, the height the ladder reaches is 10.4 ft.