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

Answer 1

To find out how high the top of the ladder reaches on the building, we can use the Pythagorean theorem. The ladder forms a right triangle with the building and the ground. In this scenario:

- The length of the ladder is the hypotenuse (c) = 24 feet.
- The distance from the base of the ladder to the building is one leg of the triangle (a) = 6 feet.
- The height the ladder reaches up the building is the other leg of the triangle (b).

According to the Pythagorean theorem:

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

Substituting the known values:

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

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

\[
36 + b^2 = 576
\]

Now, isolate \(b^2\):

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

Taking the square root of both sides gives us \(b\):

\[
b = \sqrt{540}
\]

Calculating \(\sqrt{540}\):

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

Thus, the height up the building where the ladder touches is approximately **23.24 feet**.

So, the correct response is **23.24 ft**.