A Christmas tree is supported by a wire that is 9 feet longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 41 feet shorter than the height of the tree. What is the height of the tree?

Answer
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Step 1 ：Let's denote the height of the tree as \(h\).

Step 2 ：The problem states that a wire supporting the tree is 9 feet longer than the height of the tree, so the length of the wire is \(h + 9\) feet.

Step 3 ：The wire is anchored at a point whose distance from the base of the tree is 41 feet shorter than the height of the tree, so this distance is \(h - 41\) feet.

Step 4 ：Since the wire, the tree, and the distance from the base of the tree to the point where the wire is anchored form a right triangle, we can use the Pythagorean theorem to write the equation: \((h - 41)^2 + h^2 = (h + 9)^2\).

Step 5 ：Solving this equation, we get two solutions for \(h\): 20 feet and 80 feet.

Step 6 ：However, the problem states that the distance from the base of the tree to the point where the wire is anchored is 41 feet shorter than the height of the tree. This means that the height of the tree must be greater than 41 feet.

Step 7 ：Therefore, the only possible solution is 80 feet.

Step 8 ：Final Answer: The height of the tree is \(\boxed{80}\) feet.