Question

Ben's balloon was stuck on top of a tree. To get it down, he used a 20-foot ladder and placed the bottom 12 feet away from the tree. Which of the following correctly uses a Pythagorean triple to find out how high the ladder reaches up the tree?(1 point)
Responses

14.5 feet
14.5 feet

32 feet
32 feet

8 feet
8 feet

16 feet

Answer 1

To find out how high the ladder reaches up the tree using the Pythagorean theorem, we can think of the situation as a right triangle where:

- The ladder is the hypotenuse (20 feet),
- The distance from the base of the ladder to the tree is one leg (12 feet),
- The height that the ladder reaches up the tree is the other leg, which we will call \( h \).

According to the Pythagorean theorem:

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

where
- \( a \) is one leg (12 feet),
- \( b \) is the other leg (the height \( h \)),
- \( c \) is the hypotenuse (20 feet).

Plugging in the values, we have:

\[
12^2 + h^2 = 20^2
\]

Calculating the squares:

\[
144 + h^2 = 400
\]

Now, solve for \( h^2 \):

\[
h^2 = 400 - 144
\]
\[
h^2 = 256
\]

Now, take the square root of both sides to find \( h \):

\[
h = \sqrt{256} = 16
\]

Thus, the height that the ladder reaches up the tree is **16 feet**.

The correct response is **16 feet**.