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 8 feet 8 feet 6 feet 6 feet 11.7 feet 11.7 feet 4 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 sum of the squares of the two legs is equal to the square of the hypotenuse.

In this case:
- The length of the ladder is the hypotenuse (\(c = 10\) feet).
- The distance from the base of the ladder to the tree is one leg of the triangle (\(a = 6\) feet).
- The height reached up the tree is the other leg (\(b\)).

According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]

Substituting the values we know:
\[
6^2 + b^2 = 10^2
\]
\[
36 + b^2 = 100
\]

Now, solve for \(b^2\):
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]

Taking the square root of both sides:
\[
b = 8
\]

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

The correct response is **8 feet**.