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

11.7 feet
11.7 feet

8 feet
8 feet

4 feet
4 feet

6 feet

Answer 1

To solve this problem, 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 height up the tree and the distance from the tree).

Here, let:

- \( c = 10 \) feet (length of the ladder)
- \( a = h \) (height the ladder reaches up the tree, which we need to find)
- \( b = 6 \) feet (distance from the bottom of the ladder to the tree)

According to the Pythagorean theorem:

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

Substituting the known values:

\[
h^2 + 6^2 = 10^2
\]

Calculating the squares:

\[
h^2 + 36 = 100
\]

Now, subtract 36 from both sides:

\[
h^2 = 100 - 36
\]
\[
h^2 = 64
\]

Taking the square root of both sides gives:

\[
h = 8
\]

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

So the correct response is:

**8 feet**