Question 269651
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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.)
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<pre>
We have a right angled triangle with one leg 80 ft (on the ground to the base of the three)
and other leg x, which is the height of the tree.
The hypotenuse is  (2x+11) ft, according to the problem.


So, the Pythagorean equation is 

    80^2 + x^2 = (2x+11)^2.    (1)


Simplify and reduce to the standard form quadratic equation

    6400 + x^2 = 4x^2 + 44x + 121,

    3x^2 + 44x - 6279 = 0.     (2)


The discriminant is

    d = b^2 - 4ac = 44^2 - 4*3*(-6279) = 77264, {{{sqrt(d)}}} = {{{sqrt(77264)}}} = 278.


Therefore, the solutions to equation (2)  are

    {{{x[1,2]}}} = {{{(-44 +- 278)/(2*3)}}}.


We select the positive root  x = {{{(-44 + 378)/6}}} = 39 and reject negative root.


So, the height of the three is  39 feet.    <U>ANSWER</U>.
</pre>

Solved correctly.