SOLUTION: At a point on the ground 60ft from the base of a tree, the distance to the top of the tree is 4 ft more than 2 times the height of the tree. Find the height of the tree.... I know

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Question 432571: At a point on the ground 60ft from the base of a tree, the distance to the top of the tree is 4 ft more than 2 times the height of the tree. Find the height of the tree....
I know this involves pythagorean theorem but I am stuck with factoring..I can never get it right..
3h^2+16h-3584 this is the max I can get to..need ur help in solving I cant get it thru quadratic funtion formula too pls explain in detail how to get furhter than this thanku
Answer by jorel1380(3719) (Show Source):
You can put this solution on YOUR website!
From a point on the ground, your line of sight to the top of the tree forms a right triangle from where you are to the base of the tree. Thus, 60^2+h^2=(2h+4)^2.
3600+h^2=(2h+4)^2
3600+h^2=4h^2+16h+16
0=3h^2+16h-3584
0=(3h+112)(h-32)
h=-112/3, 32
Throwing out the negative result, we get the height of the tree to be 32 ft.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=43264 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 32, -37.3333333333333. Here's your graph: