SOLUTION: At a point on the ground 70 ft from the base of a tree, the distance to the top of the tree is 2 ft more than 3 times the height of the tree. Find the height of the tree.

Question 511223: At a point on the ground 70 ft from the base of a tree, the distance to the top of the tree is 2 ft more than 3 times the height of the tree. Find the height of the tree.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
At a point on the ground 70 ft from the base of a tree, the distance to the top of the tree is 2 ft more than 3 times the height of the tree. Find the height of the tree.
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Draw the picture:
You have 2 a right triangle with base = 70,
height = h and hypotenuse = 3h+2.
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Solve for "h":
h^2 + 70^2 = (3h+2)^2
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h^2 + 4900 = 9h^2+12h+4
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8h^2 + 12h- 4896 = 0
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2h^2 + 3h - 1224 = 0
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h = [-3 +- sqrt(9 -4*2*-1224)]/4
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h = [-3 +- sqrt(9801)]/4
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Positive solution:
h = 4
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Cheers,
Stan H.
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