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
; 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

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

Answer 1

To find out how high the top of the ladder touches the building, we can use the Pythagorean theorem.

In this scenario, the ladder forms the hypotenuse of a right triangle, where:
- One leg (the distance from the wall to the base of the ladder) is 6 feet.
- The other leg (the height the ladder reaches on the building) is the height we want to find (let's call it \( b \)).
- The hypotenuse (the length of the ladder) is 24 feet.

According to the Pythagorean theorem, we have:

\[
a^2 + b^2 = c^2
\]

where:
- \( a = 6 \) feet (the distance from the wall),
- \( b \) is the height we are looking for,
- \( c = 24 \) feet (the length of the ladder).

Substituting the known values into the equation, we get:

\[
6^2 + b^2 = 24^2
\]
\[
36 + b^2 = 576
\]

Now, we can solve for \( b^2 \):

\[
b^2 = 576 - 36
\]
\[
b^2 = 540
\]

To find \( b \), take the square root:

\[
b = \sqrt{540} \approx 23.24 \text{ feet}
\]

Thus, the height of the top of the ladder on the building is approximately **23.24 feet**.

So the correct response is:

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