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

62+b2=242; 24.7 ft
6 squared plus b squared is equal to 24 squared ; 24.7 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
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Answer 1

To solve this problem, we can use the Pythagorean theorem. In this scenario, the ladder forms a right triangle with the building and the ground.

The lengths of the sides of the triangle are:

- The length of the ladder (hypotenuse): \( c = 24 \) feet
- The distance from the base of the ladder to the building (one leg of the triangle): \( a = 6 \) feet
- The height of the ladder on the building (the other leg of the triangle): \( b \)

According to the Pythagorean theorem, we have:

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

Substituting the known values into this equation:

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

Calculating \( 6^2 \) and \( 24^2 \):

\[
36 + b^2 = 576
\]

Now, subtract 36 from both sides:

\[
b^2 = 576 - 36
\]

\[
b^2 = 540
\]

To find \( b \), we take the square root of both sides:

\[
b = \sqrt{540}
\]

Calculating the square root of 540 gives us:

\[
b \approx 23.24 \text{ feet}
\]

So, the height up the building where the top of the ladder touches is approximately **23.24 feet**. Based on the options you've given, the correct response would be:

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