Final answer:
By applying the Pythagorean Theorem to the scenario of the broken tree, we calculate that the original height of the tree was 18 meters.
Step-by-step explanation:
The subject of the question is Mathematics, specifically relating to geometry and the application of the Pythagorean Theorem.
Given that a tree is broken at the height of 5 meters from the ground and that the top of the tree touches the ground 12 meters from the base, we are asked to find the original height of the tree.
To solve this, we can visualize the scenario as a right triangle, with the broken part of the tree forming the hypotenuse, the distance from the base to the point where the top touches the ground as one leg, and the remaining part of the tree standing as the other leg.
By the Pythagorean Theorem (a2 + b2 = c2), if we let 'c' be the length of the broken part (hypotenuse), 'a' be 5 meters (vertical leg), and 'b' be 12 meters (horizontal leg), we have:
52 + 122 = c2
25 + 144 = c2
169 = c2
c = sqrt(169)
c = 13 meters
Therefore, the original height of the tree is the sum of the height at which it broke (5 meters) plus the length of the broken part (13 meters), which totals to 18 meters.