SOLUTION: At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times height of the tree. Find the height of the tree.

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Question 189460: At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times height of the tree. Find the height of the tree.
Answer by nerdybill(7384) (Show Source):
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At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times height of the tree. Find the height of the tree.
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Drawing a diagram of the problem will help you "see" the solution.
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You will be applying the Pythagorean theorem.
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Let h = height of the tree
then
3h+1 is the hypotenuse
the other two sides are:
h and 35
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h^2 + 35^2 = (3h+1)^2
h^2 + 35^2 = (3h+1)(3h+1)
h^2 + 35^2 = 9h^2 + 6h + 1
35^2 = 8h^2 + 6h + 1
1225 = 8h^2 + 6h + 1
0 = 8h^2 + 6h - 1224
0 = 4h^2 + 3h - 612
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Applying the quadratic formula gives us:
h = {12, -12.75}
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Toss out the negative solution leaves us with:
h = 12 feet (height of tree)
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Details of quadratic follows:

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=9801 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, -12.75. Here's your graph: