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

• 8 feet
• 4 feet
• 6 feet
• 11.7 feet

Answer 1

To determine how high the ladder reaches up the tree, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ladder is the hypotenuse measuring 10 feet, the distance from the bottom of the ladder to the tree is one leg measuring 6 feet, and the height that the ladder reaches up the tree is the other leg (let's call it \( h \)).

According to the Pythagorean theorem:

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

Calculating the squares:

\[ h^2 + 36 = 100 \]

Subtracting 36 from both sides:

\[ h^2 = 100 - 36 \] \[ h^2 = 64 \]

Taking the square root of both sides gives:

\[ h = 8 \]

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