Question

a 50 foot ladder is set against the side of a house so that it reaches up 48 feet. if jack 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 44 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 \(c = 50\), \(b = 48\). Let initial base distance be \(x\). So \(x^2+48^2 = 50^2\).
\(x^2=50^2 - 48^2=(50 - 48)(50 + 48)=2\times98 = 196\), so \(x = 14\) feet.

Step2: Find new base distance

After pulling 4 feet farther, new base distance \(y=14 + 4=18\) feet.

Step3: Find new height

Let new height be \(h\). Using Pythagorean theorem again: \(h^2+18^2 = 50^2\).
\(h^2=50^2 - 18^2=(50 - 18)(50 + 18)=32\times68 = 2176\).
\(h=\sqrt{2176}\approx46.6\) feet.

Answer:

\(46.6\)