SOLUTION: At a point on the ground 80 ft from the base of a​ tree, the distance to the top of the tree is 11 ft more than 2 times the height of the tree. Find the height of the tree.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: At a point on the ground 80 ft from the base of a​ tree, the distance to the top of the tree is 11 ft more than 2 times the height of the tree. Find the height of the tree.       Log On


   

Question 1066820: At a point on the ground 80 ft from the base of a​ tree, the distance to the top of the tree is 11 ft more than 2 times the height of the tree. Find the height of the tree.
The height of the tree is blank ft.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
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The hypotenuse is 2x+11
square the legs and make the sum equal to the square of the hypotenuse and solve the quadratic.
x^2+80^2=(2x+11)^2
x^2+6400=4x^2+44x+121
0=3x^2+44x-6279
x=(1/6)(-44+/- sqrt (77,284); sqrt (77,284)=278
x=(1/6)+234=39
The tree is 39 feet tall
The hypotenuse is 89 feet.
It is a 39/80/89 right triangle
1521+6400=7921, and that is 89^2.