Question
The bottom of a ladder must be placed 5 feet from a building. The ladder is 14 feet long. How far above the ground does the ladder touch the wall?
Answers
GPT 3.5
To solve this problem, we can use the Pythagorean theorem. Let's label the distance above the ground that the ladder touches the wall as "x".
According to the Pythagorean theorem, the square of the hypotenuse (which is the ladder) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 14 feet (the length of the ladder), one side is x feet (height above the ground), and the other side is 5 feet (the distance of the bottom of the ladder from the building).
So, using the Pythagorean theorem, we have:
14^2 = x^2 + 5^2
196 = x^2 + 25
Next, we can rearrange the equation:
x^2 = 196 - 25
x^2 = 171
Taking the square root of both sides:
x = √171
x ≈ 13.08
Therefore, the ladder touches the wall at a height of approximately 13.08 feet above the ground.
According to the Pythagorean theorem, the square of the hypotenuse (which is the ladder) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 14 feet (the length of the ladder), one side is x feet (height above the ground), and the other side is 5 feet (the distance of the bottom of the ladder from the building).
So, using the Pythagorean theorem, we have:
14^2 = x^2 + 5^2
196 = x^2 + 25
Next, we can rearrange the equation:
x^2 = 196 - 25
x^2 = 171
Taking the square root of both sides:
x = √171
x ≈ 13.08
Therefore, the ladder touches the wall at a height of approximately 13.08 feet above the ground.