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

8 feet
8 feet

4 feet
4 feet

11.7 feet
11.7 feet

6 feet

Answer 1

To determine how high the ladder reaches up the tree, we can apply the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the lengths of the other two sides (the height of the tree and the distance from the base of the ladder to the tree).

In this problem:

• The length of the ladder (hypotenuse) is 10 feet.
• The distance from the bottom of the ladder to the tree (one leg) is 6 feet.
• The height the ladder reaches up the tree (the other leg) is unknown.

We can set up the equation as follows:

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

Where:

• \(a\) is the height the ladder reaches up the tree (unknown),
• \(b\) is the distance from the base of the ladder to the tree (6 feet),
• \(c\) is the length of the ladder (10 feet).

Substituting the known values:

\[ a^2 + 6^2 = 10^2 \] \[ a^2 + 36 = 100 \] \[ a^2 = 100 - 36 \] \[ a^2 = 64 \] \[ a = \sqrt{64} \] \[ a = 8 \]

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

Thus, the correct response is:

8 feet