Answer :
Answer:
The answer is A. 14.8 feet.
Explanation:
We can use the Pythagorean theorem to solve this problem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder represents the hypotenuse, and the distance from the building and the height reached by the ladder represent the other two sides.
Let's denote:
- [tex]\( a \)[/tex] as the distance from the building to the base of the ladder (6 feet)
- [tex]\( b \)[/tex] as the height reached by the ladder up the building (what we need to find)
- [tex]\( c \)[/tex] as the length of the ladder (16 feet)
According to the Pythagorean theorem, we have:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Substituting the given values:
[tex]\[ 6^2 + b^2 = 16^2 \][/tex]
[tex]\[ 36 + b^2 = 256 \][/tex]
[tex]\[ b^2 = 256 - 36 \][/tex]
[tex]\[ b^2 = 220 \][/tex]
To find [tex]\( b \)[/tex], we take the square root of both sides:
[tex]\[ b = \sqrt{220} \][/tex]
Using a calculator, we find:
[tex]\[ b \approx 14.8 \][/tex]
So, the ladder can reach up to approximately 14.8 feet on the building to help save the cat.
