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
The ladder, the building, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the building to the point where the ladder touches the ground is one leg of the triangle, and the height up the building to the top of the ladder is the other leg of the triangle.
Using the Pythagorean theorem, we can calculate the height up the building:
a^2 + b^2 = c^2
where a = distance from the building to the point where the ladder touches the ground = 6 feet, b = height up the building to the top of the ladder, and c = length of the ladder = 24 feet.
Plugging in the values:
6^2 + b^2 = 24^2
36 + b^2 = 576
b^2 = 540
b = √540
b ≈ 23.24 feet
So, the top of the ladder is approximately 23.24 feet up the building.
Using the Pythagorean theorem, we can calculate the height up the building:
a^2 + b^2 = c^2
where a = distance from the building to the point where the ladder touches the ground = 6 feet, b = height up the building to the top of the ladder, and c = length of the ladder = 24 feet.
Plugging in the values:
6^2 + b^2 = 24^2
36 + b^2 = 576
b^2 = 540
b = √540
b ≈ 23.24 feet
So, the top of the ladder is approximately 23.24 feet up the building.