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.

Answer 1

Initial horizontal distance = sqrt(40^2 − 24^2) = sqrt(1600 − 576) = sqrt(1024) = 32 ft.
After pulling 4 ft farther, new base distance = 32 + 4 = 36 ft.
New height = sqrt(40^2 − 36^2) = sqrt(1600 − 1296) = sqrt(304) ≈ 17.4356 ft.

Rounded to the nearest tenth: 17.4 ft.