Question
If you have a 24 foot ladder that is leaning against the building and touching the ground 6 feet from the building. How high up the building is the top of the ladder?
Answers
GPT 3.5
To find the height up the building that the top of the ladder reaches, we can use the Pythagorean theorem.
In this scenario, the ladder, the building, and the ground form a right-angled triangle. The ladder is the hypotenuse, the height up the building is one of the legs, and the distance from the building to where the ladder touches the ground is the other leg.
Let's designate the height up the building as "h". According to the Pythagorean theorem, the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Therefore, h^2 + 6^2 = 24^2
h^2 + 36 = 576
h^2 = 576 - 36
h^2 = 540
h = √540
h ≈ 23.2
So, the top of the ladder is approximately 23.2 feet up the building.
In this scenario, the ladder, the building, and the ground form a right-angled triangle. The ladder is the hypotenuse, the height up the building is one of the legs, and the distance from the building to where the ladder touches the ground is the other leg.
Let's designate the height up the building as "h". According to the Pythagorean theorem, the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Therefore, h^2 + 6^2 = 24^2
h^2 + 36 = 576
h^2 = 576 - 36
h^2 = 540
h = √540
h ≈ 23.2
So, the top of the ladder is approximately 23.2 feet up the building.