Question

A 30-foot ladder is set against the side of a house so that it reaches up 24 feet. If Elizabeth 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 21 ft.) Round to the nearest tenth of a foot.

Answer 1

Use the Pythagorean theorem to calculate the distance from the wall the ladder originally is:

x = sqrt(30^2 - 24^2)

x = sqrt(900-576)

x = sqrt(324)

x = 18

The ladder was originally 18 feet from the wall. Moving the ladder 3 feet further away makes the new distance 18 + 3 = 21 feet.

Now use the Pythagorean theorem again to find the new height of the ladder.

Height = sqrt(30^2 - 21^2)

Height = sqrt(900 - 441)

Height = sqrt(459)

Height = 21.42

Rounded to the nearest tenth = 21.4 feet.