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)

Question

Responses

6 feet
6 feet

8 feet
8 feet

4 feet
4 feet

11.7 feet
11.7 feet

Answer 1

To find out how high the ladder reaches up the tree using the Pythagorean theorem, we can consider the situation as a right triangle.

The ladder itself acts as the hypotenuse (c), which is 10 feet long, while the distance from the bottom of the ladder to the base of the tree (the base of the triangle, a) is 6 feet. The height the ladder reaches up the tree (the height of the triangle, b) is what we need to find.

According to the Pythagorean theorem:

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

Substituting the known values into the equation:

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

This simplifies to:

\[ 36 + b^2 = 100 \]

Now, isolate \( b^2 \):

\[ b^2 = 100 - 36 \]

\[ b^2 = 64 \]

Now, take the square root of both sides:

\[ b = \sqrt{64} \]

\[ b = 8 \]

So, the height of the ladder up the tree is 8 feet.

Therefore, the correct response is:

8 feet.