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

a. b. c. or d.?

Answer 1

To solve the problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case:
- The length of the ladder (hypotenuse) is \( c = 24 \) feet.
- The distance from the building to the base of the ladder (one side) is \( b = 6 \) feet.
- The height up the building (the other side) is \( a \).

According to the Pythagorean theorem, we have:

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

Substituting the known values into the equation:

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

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

\[
a^2 + 36 = 576
\]

Now, we can isolate \( a^2 \):

\[
a^2 = 576 - 36
\]

Calculating the right side:

\[
a^2 = 540
\]

Taking the square root of both sides to find \( a \):

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

Therefore, the height up the building at the top of the ladder is approximately **23.24 feet**.

Now looking at your response options, the correct answer would be **23.24 ft** (option b or c depending on your list).