SOLUTION: 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

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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.)

Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
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.)
let the height of the tree be x
horizontal distance from the tree is 80 feet
distance to the top of the tree is 2x+11
using the pythagoras theorem we get
(x+2)^2= x^2 + 80^2
x^2+4x+4=x^2 +80^2
x^2-x^2 +4x=80^2
4x=80^2
x=80^2 /4
x= 80^20
x=1600
the height of the tree is 1600 feet.

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
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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        The governing equation in the post by @mananth is incorrect.
        As a consequence of it, all his calculations are irrelevant and his answer is absurdist.

        I came to bring a correct solution.

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, = = 278. Therefore, the solutions to equation (2) are = . We select the positive root x = = 39 and reject negative root. So, the height of the three is 39 feet. ANSWER.

Solved correctly.

Answer by n2(78)   (Show Source):
You can put this solution on YOUR website!
.
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.)
~~~~~~~~~~~~~~~~~~~~~~~~~~~

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, = = 278. Therefore, the solutions to equation (2) are = . We select the positive root x = = 39 and reject negative root. So, the height of the three is 39 feet. ANSWER.

Solved correctly.