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

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

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

a2+242=62
; 23.24 ft
A squared plus 24 squared is equal to 6 squared ; 23.24 ft
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Answer 1

To find how high the top of the ladder is on the building, we can use the Pythagorean theorem, which states:

\( a^2 + b^2 = c^2 \)

where:
- \( a \) is the height up the building (which we are trying to find),
- \( b \) is the distance from the building to the base of the ladder (6 feet in this case),
- \( c \) is the length of the ladder (24 feet).

Substituting in the known values:

1. \( a^2 + 6^2 = 24^2 \)
2. \( a^2 + 36 = 576 \) (since \( 6^2 = 36 \) and \( 24^2 = 576 \))
3. \( a^2 = 576 - 36 \)
4. \( a^2 = 540 \)
5. \( a = \sqrt{540} \)
6. \( a \approx 23.24 \) feet

So the height of the top of the ladder on the building is approximately **23.24 ft**.

The correct answer from the options provided is:

**6 squared plus b squared is equal to 24 squared; 23.24 ft**.