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?
To find out how high the ladder reaches up the tree, we can use the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the bottom of the ladder to the tree represents one side, and the height of the ladder represents the other side.
Let's first find a Pythagorean triple that includes the number 10 (the length of the ladder).
One Pythagorean triple that includes 10 is 6-8-10.
This means that one of the sides of the triangle (the distance from the bottom of the ladder to the tree) is 6 feet, and the other side (the height of the ladder) is 8 feet.
Therefore, the ladder reaches up the tree to a height of 8 feet.
The correct answer is:
8 feet