Question

A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jace grabs the ladder at its base and pulls it 7 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 41 ft.) Round to the nearest tenth of a foot.

Answer 1

Let the distance from the house to the ladder's base be x. Initially,
x = sqrt(52^2 − 48^2) = sqrt(2704 − 2304) = sqrt(400) = 20 ft.

After pulling the base 7 ft farther, the base is 20 + 7 = 27 ft from the house. The new height h is
h = sqrt(52^2 − 27^2) = sqrt(2704 − 729) = sqrt(1975) ≈ 44.44097 ft.

Rounded to the nearest tenth: 44.4 ft.