SOLUTION: At a point on the ground 12 ft from the base of the tree, the distance to the top of the tree is 3 ft more than 2 times the heiht of the tree. Find the height of the tree.

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Question 942255: At a point on the ground 12 ft from the base of the tree, the distance to the top of the tree is 3 ft more than 2 times the heiht of the tree. Find the height of the tree.
Answer by stanbon(75887) (Show Source):
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At a point on the ground 12 ft from the base of the tree, the distance to the top of the tree is 3 ft more than 2 times the heiht of the tree. Find the height of the tree.
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Draw and label the picture::
You have a right triangle:
base = 12 ft
height = h ft
hypotenuse = 2h+3 ft
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Use Pythagoras::
h^2 + 12^2 = (2h+3)^2
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h^2 + 144 = 4h^2 + 12h + 9
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3h^2 +12h - 135 = 0
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h^2 + 4h - 45 = 0
Factor::
(h-5)(h+9) = 0
Positive solution::
height = 5 ft
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Cheers,
Stan H.
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