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?
A Pythagorean triple is a set of three positive integers that satisfy the Pythagorean theorem, a^2 + b^2 = c^2.
In this case, we have a right triangle with one leg of 6 feet (the distance from the base of the tree to the ladder) and another leg of h feet (the height the ladder reaches up the tree). The ladder itself is the hypotenuse of the right triangle.
One Pythagorean triple that can be used to find the height of the ladder is the 3-4-5 triple. This means that the legs of the triangle are 3 feet and 4 feet, and the hypotenuse is 5 feet.
In this case, since one leg is 6 feet and we want to find the height of the ladder, we can use the multiple of the 3-4-5 triple to solve for the height:
6 = 2*3
So, the height of the ladder is 2*5 = 10 feet.
Therefore, the ladder reaches up the tree to a height of 10 feet.