SOLUTION: A Christmas tree is supported by a wire that is 6 feet longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 42 feet short

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Question 1193171: A Christmas tree is supported by a wire that is 6 feet longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 42 feet shorter than the height of the tree. What is the height of the tree?
Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


Assuming that the tree, the ground, and the wire form a right triangle, the legs are x and x-42, and the hypotenuse is x+6.

x%5E2%2B%28x-42%29%5E2=%28x%2B6%29%5E2
x%5E2%2Bx%5E2-84x%2B1764=x%5E2%2B12x%2B36
x%5E2-96x%2B1728=0
%28x-72%29%28x-24%29=0

x is either 72 or 24; but x=24 makes no sense.

So x=72.

ANSWER: the height of the tree is 72 feet