Final answer:
Using the Pythagorean theorem, the ladder, which is 14 meters in length and whose base is 4 meters away from the tree, reaches approximately 13 meters up the tree. Option A is the correct answer.
Step-by-step explanation:
The problem presented in the question is a standard application of the Pythagorean theorem, involving a ladder leaning against a tree. The ladder serves as the hypotenuse, the distance from the base of the ladder to the tree is one leg, and the other leg is the height up the tree where the ladder reaches.
The length of the ladder is given as 14 meters, and the base of the ladder is 4 meters away from the base of the tree. To find the height the ladder reaches up the tree (the other leg of the right triangle), we use the Pythagorean theorem (a^2 + b^2 = c^2), where:
Plugging in the values we have:
4^2 + b^2 = 14^2
16 + b^2 = 196
b^2 = 196 - 16
b^2 = 180
b = sqrt(180)
b = 13.416 meters (approximately)
The closest whole number to 13.416 meters is 13 meters, so the height the ladder reaches up the tree is approximately 13 meters. This corresponds with option A among the given options: A. 13 meters, B. 14 meters, C. 15 meters, D. 16 meters.