Question

A 51 foot ladder is set against the side of a house so that it reaches up 45 feet. If Nora grabs the ladder at its base and pulls it 6 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 39 ft.) Round to the nearest tenth of a foot.

Answer 1

Use the Pythagorean theorem. Initially the base is sqrt(51^2 − 45^2) = sqrt(2601 − 2025) = sqrt(576) = 24 ft. After pulling 6 ft, the base is 24 + 6 = 30 ft, so the new height is

sqrt(51^2 − 30^2) = sqrt(2601 − 900) = sqrt(1701) ≈ 41.243…

Rounded to the nearest tenth: 41.2 ft.