Question

A 45 foot ladder is set against the side of a house so that it reaches up 27 feet. If Cooper 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 23 ft.) Round to the nearest tenth of a foot.

Answer 1

42 feets

Explanation:

We consider the right-angle triangle with B being the right-angle:

AB = 24 ft ; AC = 45 ft

We can use the Pythagorean theorem:

`AB^(2) = AB^(2) + BC^(2) \\45^(2) = 24^(2) + BC^(2) \\BC^(2) = 2025 - 576\\BC = √(1449) = 38`

The distance between the wall and the ladder is 38 feet.

Pulling the ladder away from the wall is adding 4 feet to the distance between the wall and the ladder.

38 + 4 = 42

The ladder is now 48 feet away from the wall at its bottom.