Question

Christian’s kite was stuck on top of a tree. To get it down, he used a 10-foot ladder and placed the bottom 6 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

6 feet
6 feet

11.7 feet
11.7 feet

4 feet
4 feet

8 feet

Answer 1

To find out how high the ladder reaches up 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) is equal to the sum of the squares of the other two sides (the height up the tree and the distance from the base of the ladder to the tree).

Let's denote:
- The height the ladder reaches up the tree as \( h \)
- The distance from the base of the ladder to the tree as \( 6 \) feet
- The length of the ladder as \( 10 \) feet

According to the Pythagorean theorem:
\[ h^2 + 6^2 = 10^2 \]

Now, calculate \( 6^2 \) and \( 10^2 \):
\[ h^2 + 36 = 100 \]

Now, isolate \( h^2 \):
\[ h^2 = 100 - 36 \]
\[ h^2 = 64 \]

Taking the square root of both sides gives:
\[ h = \sqrt{64} \]
\[ h = 8 \]

So, the height the ladder reaches up the tree is **8 feet**.

Thus, the correct response is:
**8 feet**.