Question

a 25 foot ladder is set against the side of a house so that it reaches up 15 feet. if camden 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 12 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 \(c = 25\) (ladder), \(b = 15\) (height). So \(a^2 + 15^2 = 25^2\).
\(a^2 = 25^2 - 15^2 = 625 - 225 = 400\), so \(a = 20\) feet (initial base distance).

Step2: Find new base distance

Pulled 3 feet farther, so new base distance \(= 20 + 3 = 23\) feet.

Step3: Find new height

Again use Pythagorean theorem: \(23^2 + b^2 = 25^2\).
\(b^2 = 25^2 - 23^2 = 625 - 529 = 96\).
\(b = \sqrt{96} \approx 9.8\) feet (rounded to nearest tenth).

Answer:

\(9.8\) feet