A 45-foot ladder is initially placed against a house, reaching 27 feet up the wall. The base of the ladder is then pulled 4 feet further away from the house. We need to find the new height the ladder reaches on the wall, rounded to the nearest tenth of a foot.

1. Problem Description

A 45-foot ladder is initially placed against a house, reaching 27 feet up the wall. The base of the ladder is then pulled 4 feet further away from the house. We need to find the new height the ladder reaches on the wall, rounded to the nearest tenth of a foot.

2. Solution Steps

First, we need to find the initial distance of the base of the ladder from the house. We can use the Pythagorean theorem for this. Let $a$ be the initial distance of the base from the house, and $b$ be the initial height the ladder reaches. The ladder itself is the hypotenuse $c$. We have $b = 27$ and $c = 45$.

The Pythagorean theorem states that:

$a^2 + b^2 = c^2$

$a^2 + 27^2 = 45^2$

$a^2 + 729 = 2025$

$a^2 = 2025 - 729$

$a^2 = 1296$

$a = \sqrt{1296}$

$a = 36$

So, the initial distance of the base of the ladder from the house is 36 feet.

Now, the base of the ladder is pulled 4 feet farther away. The new distance from the house is $36 + 4 = 40$ feet.

Let $b'$ be the new height the ladder reaches. The length of the ladder remains the same at 45 feet. Again, we use the Pythagorean theorem:

$a'^2 + b'^2 = c^2$

$40^2 + b'^2 = 45^2$

$1600 + b'^2 = 2025$

$b'^2 = 2025 - 1600$

$b'^2 = 425$

$b' = \sqrt{425}$

$b' \approx 20.6155$

Rounding to the nearest tenth of a foot, we get $b' \approx 20.6$ feet.

3. Final Answer

The ladder will now reach approximately 20.6 feet up the side of the house.