Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable,

Question

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.
108 ft.
10.4 ft.
180 ft.

Answer 1

To find out how high the ladder will reach on the house using the Pythagorean Theorem, we can represent the situation as a right triangle, where:

• The length of the ladder (hypotenuse) is 12 ft.
• The distance from the base of the house to the bottom of the ladder (one leg) is 6 ft.
• The height the ladder reaches on the house (the other leg) is what we need to find.

The Pythagorean Theorem states that:

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

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.

Let:

• \(a = 6\) ft (the distance from the wall)
• \(b\) = height we need to find
• \(c = 12\) ft (the length of the ladder)

Plugging the values into the equation:

\[ 6^2 + b^2 = 12^2 \] \[ 36 + b^2 = 144 \] \[ b^2 = 144 - 36 \] \[ b^2 = 108 \] \[ b = \sqrt{108} \] \[ b \approx 10.4 \text{ ft (when rounded to the nearest tenth)} \]

Thus, the height the ladder will reach is approximately 10.4 ft.

The correct answer is 10.4 ft.