Question
If the bottom of a 5.0 m ladder is 1.6m from a wall, how high on the wall does it reach?
Answers
GPT 3.5
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with the ladder being the hypotenuse, the distance between the ladder and the wall as one side, and the height on the wall as the other side.
Using the Pythagorean theorem, we can calculate the height on the wall:
(height on the wall)^2 = (length of ladder)^2 - (distance between ladder and wall)^2
= 5.0^2 - 1.6^2
= 25 - 2.56
= 22.44
Now, we can find the square root of 22.44 to determine the height on the wall:
height on the wall ≈ √22.44
≈ 4.74 m
Therefore, the ladder reaches approximately 4.74 meters high on the wall.
In this case, we have a right triangle with the ladder being the hypotenuse, the distance between the ladder and the wall as one side, and the height on the wall as the other side.
Using the Pythagorean theorem, we can calculate the height on the wall:
(height on the wall)^2 = (length of ladder)^2 - (distance between ladder and wall)^2
= 5.0^2 - 1.6^2
= 25 - 2.56
= 22.44
Now, we can find the square root of 22.44 to determine the height on the wall:
height on the wall ≈ √22.44
≈ 4.74 m
Therefore, the ladder reaches approximately 4.74 meters high on the wall.