Question

a 30 foot ladder is set against the side of a house so that it reaches up 24 feet. if elizabeth grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (the answer is not 21 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 \(c = 30\) (ladder), \(b = 24\) (height). Let \(a\) be base. So \(a^2 + 24^2 = 30^2\).
\(a^2 = 30^2 - 24^2 = 900 - 576 = 324\), so \(a = \sqrt{324} = 18\) feet.

Step2: Find new base distance

Pulled 3 feet farther, so new base \(a' = 18 + 3 = 21\) feet.

Step3: Find new height

Again use Pythagorean theorem. Let \(b'\) be new height. \(21^2 + (b')^2 = 30^2\).
\((b')^2 = 30^2 - 21^2 = 900 - 441 = 459\).
\(b' = \sqrt{459} \approx 21.4\) feet (rounded to nearest tenth).

Answer:

\(21.4\) feet