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While painting the side of his house, Jason positioned his ladder so that the top was $16$ feet above the ground, while the bottom was $12$ feet away from the base of the wall. To reach a spot higher up on the house, Jason moved the ladder so that the top was $18$ feet above the ground. How much closer to the house is the bottom of the ladder now? If necessary, round your answer to the nearest tenth. $\newline$ ____ feet

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Pythagorean theorem

Full solution

Q. While painting the side of his house, Jason positioned his ladder so that the top was

16

feet above the ground, while the bottom was

12

feet away from the base of the wall. To reach a spot higher up on the house, Jason moved the ladder so that the top was

18

feet above the ground. How much closer to the house is the bottom of the ladder now? If necessary, round your answer to the nearest tenth.

\newline

____ feet

Identify Setup and Length: Identify the initial setup of the ladder and use the Pythagorean theorem to find the ladder's length.
Calculate New Position: Calculate the new position of the bottom of the ladder using the same ladder length $l$ and the new height $h$ .
Determine Closer Distance: Determine how much closer the ladder is to the house after being moved.

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