Final answer:
To solve the problem, assign the variable h for tree height and create an equation representing a right triangle formed with the ground and the distance to the top of the tree. By solving the equation using Pythagorean theorem, we determine the height of the tree to be 15 feet.
Step-by-step explanation:
The problem involves finding the height of a tree using a given relationship between the height of the tree, the distance from the tree, and the distance of the top of the tree from a certain point on the ground. To solve this problem, we can apply Pythagorean Theorem or set up an algebraic equation.
Steps to Solve the Problem
Let the height of the tree be h feet.
According to the problem, the distance from the top of the tree to the point on the ground is 2h + 3.
As the distance to the base of the tree is 12 feet, we form a right-angled triangle where one leg is h (height of the tree), the other leg is 12 feet, and the hypotenuse is 2h + 3.
Applying Pythagorean theorem,
(h)2 + (12)2 = (2h + 3)2.
Solve this quadratic equation to find the value of h.
After solving, the quadratic equation yields h = 15 feet as the height of the tree.