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

242+62=c2
; 24.7 ft
24 squared plus 6 squared is equal to c squared ; 24.7 ft

62+b2=242
; 24.7 ft
6 squared plus b squared is equal to 24 squared ; 24.7 ft

62+b2=242
; 23.24 ft
6 squared plus b squared is equal to 24 squared ; 23.24 ft

a2+242=62
; 23.24 ft
A squared plus 24 squared is equal to 6 squared ; 23.24 ft

Answer 1

24 squared plus 6 squared is equal to c squared

576 + 36 = c squared

612 = c squared

c = 24.7 ft

Therefore, the top of the ladder is approximately 24.7 feet up the building.

Answer 2

but wouldn't 24 represent the hypotenuse since the ladder is leaning? just askin

Answer 3

Yes, you are correct! Since the ladder is leaning against the building, the ladder itself represents the hypotenuse of a right triangle. Therefore, the length of the ladder (24 ft) would represent the hypotenuse, and the height up the building would be one of the legs of the right triangle.

Let's use the Pythagorean theorem to solve for the height up the building (b):

a^2 + b^2 = c^2

6^2 + b^2 = 24^2

36 + b^2 = 576

b^2 = 540

b ≈ 23.24 ft

Therefore, the top of the ladder is approximately 23.24 feet up the building. Thank you for pointing that out!