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

16 feet
16 feet

8 feet
8 feet

32 feet

Answer 1

To find out how high the ladder reaches on the tree, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the lengths of the other two sides (the distance from the wall and the height up the tree).

Given:
- The length of the ladder (hypotenuse) = 20 feet
- The distance from the base of the ladder to the tree (one side of the triangle) = 12 feet
- The height up the tree (the other side we need to find) = x feet

Using the Pythagorean theorem:
\[
x^2 + 12^2 = 20^2
\]

Calculating \(12^2\) and \(20^2\):
\[
x^2 + 144 = 400
\]

Now, isolate \(x^2\):
\[
x^2 = 400 - 144
\]
\[
x^2 = 256
\]

Now take the square root of both sides to find \(x\):
\[
x = \sqrt{256}
\]
\[
x = 16
\]

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

The correct response is:
**16 feet**