Question

a 45 foot ladder is set against the side of a house so that it reaches up 27 feet. if latanya 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 24 ft.) round to the nearest tenth of a foot.

Explanation:

Step1: Find initial distance from house

Using Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c = 45\) (ladder), \(b = 27\) (height). Let \(a\) be initial distance from house.
\(a^2 + 27^2 = 45^2\)
\(a^2 = 45^2 - 27^2\)
\(a^2 = 2025 - 729 = 1296\)
\(a = \sqrt{1296} = 36\) feet.

Step2: Find new distance from house

Latanya pulls ladder 3 feet farther, so new distance \(a_{new} = 36 + 3 = 39\) feet.

Step3: Find new height

Let new height be \(b_{new}\). Using Pythagorean theorem again:
\(39^2 + b_{new}^2 = 45^2\)
\(b_{new}^2 = 45^2 - 39^2\)
\(b_{new}^2 = 2025 - 1521 = 504\)
\(b_{new} = \sqrt{504} \approx 22.4\) feet (rounded to nearest tenth).

Answer:

22.4 feet