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?
(1 point)
Responses
24^2+6^2=c^2; 24.7 ft
24 squared plus 6 squared is equal to c squared ; 24.7 ft
6^2+b^2=24^2; 24.7 ft
6 squared plus b squared is equal to 24 squared ; 24.7 ft
a^2+24^2=6^2; 23.24 ft
6^2+b^2=24^2; 23.24ft
(1 point)
Responses
24^2+6^2=c^2; 24.7 ft
24 squared plus 6 squared is equal to c squared ; 24.7 ft
6^2+b^2=24^2; 24.7 ft
6 squared plus b squared is equal to 24 squared ; 24.7 ft
a^2+24^2=6^2; 23.24 ft
6^2+b^2=24^2; 23.24ft
Answers
GPT 3.5
24^2 + 6^2 = c^2
576 + 36 = c^2
612 = c^2
c = √612
c ≈ 24.7 ft
Therefore, the top of the ladder is approximately 24.7 feet high up the building.
576 + 36 = c^2
612 = c^2
c = √612
c ≈ 24.7 ft
Therefore, the top of the ladder is approximately 24.7 feet high up the building.
Choose the correct answer and explain it
GPT 3.5
The correct answer is:
24^2 + 6^2 = c^2; 24.7 ft
This solution uses the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder leaning against the building forms a right triangle with the ladder being the hypotenuse. By plugging in the values of the ladder length (24 ft) and the distance away from the building (6 ft) into the formula, we can solve for the height of the ladder (c), which is approximately 24.7 ft.
24^2 + 6^2 = c^2; 24.7 ft
This solution uses the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder leaning against the building forms a right triangle with the ladder being the hypotenuse. By plugging in the values of the ladder length (24 ft) and the distance away from the building (6 ft) into the formula, we can solve for the height of the ladder (c), which is approximately 24.7 ft.