Question

a 40 foot ladder is set against the side of a house so that it reaches up 24 feet. if lily grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (the answer is not 20 ft.) round to the nearest tenth of a foot.

Explanation:

Step1: Find initial base distance

Using Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c = 40\) (ladder length) and \(b = 24\) (height on house). Let initial base distance be \(x\). So \(x^2 + 24^2 = 40^2\). Calculating \(x^2 = 40^2 - 24^2 = 1600 - 576 = 1024\). Thus \(x = \sqrt{1024} = 32\) feet.

Step2: Find new base distance

After pulling 4 feet farther, new base distance \(y = 32 + 4 = 36\) feet.

Step3: Find new height on house

Let new height be \(h\). Using Pythagorean theorem again: \(h^2 + 36^2 = 40^2\). So \(h^2 = 40^2 - 36^2 = 1600 - 1296 = 304\). Then \(h = \sqrt{304} \approx 17.4\) feet (rounded to nearest tenth).

Answer:

\(17.4\) feet