To find out how high the ladder reaches on the tree, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the lengths of the other two sides (the distance from the wall and the height up the tree).
Given:
- The length of the ladder (hypotenuse) = 20 feet
- The distance from the base of the ladder to the tree (one side of the triangle) = 12 feet
- The height up the tree (the other side we need to find) = x feet
Using the Pythagorean theorem: \[ x^2 + 12^2 = 20^2 \]
Calculating \(12^2\) and \(20^2\): \[ x^2 + 144 = 400 \]
Now, isolate \(x^2\): \[ x^2 = 400 - 144 \] \[ x^2 = 256 \]
Now take the square root of both sides to find \(x\): \[ x = \sqrt{256} \] \[ x = 16 \]
Thus, the height the ladder reaches up the tree is 16 feet.
The correct response is: 16 feet