document.write( "Question 269651: At a point on the ground 80ft from the base of a tree, the distance to the top of the tree is 11ft more than 2 times the height of the tree. Find the height of the tree. (Simplify your answer. Round to the nearest foot as needed.)\r
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Algebra.Com's Answer #854079 by n2(78) $\"\"$ $\"About$

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\n" ); document.write( "At a point on the ground 80ft from the base of a tree, the distance to the top of the tree is 11ft more than 2 times
\n" ); document.write( "the height of the tree. Find the height of the tree. (Simplify your answer. Round to the nearest foot as needed.)
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document.write( "We have a right angled triangle with one leg 80 ft (on the ground to the base of the three)\r\n" );
document.write( "and other leg x, which is the height of the tree.\r\n" );
document.write( "The hypotenuse is  (2x+11) ft, according to the problem.\r\n" );
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document.write( "So, the Pythagorean equation is \r\n" );
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document.write( "    80^2 + x^2 = (2x+11)^2.    (1)\r\n" );
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document.write( "Simplify and reduce to the standard form quadratic equation\r\n" );
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document.write( "    6400 + x^2 = 4x^2 + 44x + 121,\r\n" );
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document.write( "    3x^2 + 44x - 6279 = 0.     (2)\r\n" );
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document.write( "The discriminant is\r\n" );
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document.write( "    d = b^2 - 4ac = 44^2 - 4*3*(-6279) = 77264,  =  = 278.\r\n" );
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document.write( "Therefore, the solutions to equation (2)  are\r\n" );
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document.write( "     = .\r\n" );
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document.write( "We select the positive root  x =  = 39 and reject negative root.\r\n" );
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document.write( "So, the height of the three is  39 feet.    ANSWER.\r\n" );
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