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