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.
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.
Ask by Boone Luna. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After pulling the ladder 4 feet farther from the house, it reaches approximately 20.6 feet up the side of the house.
Solution
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Beyond the Answer
To solve this, we can use the Pythagorean theorem. Initially, the ladder forms a right triangle where the ladder is the hypotenuse (45 ft), the height it reaches up the house is one leg (27 ft), and the distance from the base of the ladder to the house is the other leg.
Using the Pythagorean theorem:
-
Find the original distance from the base of the ladder to the house:
whereft and ft.
ft. -
Now, when Cooper pulls the ladder 4 ft farther away from the house, the new base distance is
ft. -
Now, using the Pythagorean theorem again to find the new height (
):
ft.
So after pulling the ladder 4 feet farther from the house, it will reach approximately 20.7 feet up the side of the house.
