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# Algebra Question

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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.

The height of the tree is nothing  ft.

yojaymarojas  May 13, 2017

#1
+4155
+4

Here, h is the height of the tree.

from the Pythagorean theorem:

h2 + 802 = (11 + 2h)2

h2 + 6400 = (11 + 2h)(11 + 2h)

h2 + 6400 = 121 + 44h + 4h2            Subtract h2 and 6400 from both sides.

0 = -6279 + 44h + 3h2                      Rearrange.

0 = 3h2 + 44h - 6279                        Use quadratic formula to solve for h.

$$h = {-44 \pm \sqrt{44^2-4(3)(-6279)} \over 2(3)} \\~\\ h = \frac{-44\pm278}{6} \\~\\ h=\frac{-44+278}{6}=39 \qquad\text{or}\qquad h=\frac{-44-278}{6}=-\frac{161}3$$

So...the height of the tree must be 39 feet

hectictar  May 13, 2017
Sort:

#1
+4155
+4

Here, h is the height of the tree.

from the Pythagorean theorem:

h2 + 802 = (11 + 2h)2

h2 + 6400 = (11 + 2h)(11 + 2h)

h2 + 6400 = 121 + 44h + 4h2            Subtract h2 and 6400 from both sides.

0 = -6279 + 44h + 3h2                      Rearrange.

0 = 3h2 + 44h - 6279                        Use quadratic formula to solve for h.

$$h = {-44 \pm \sqrt{44^2-4(3)(-6279)} \over 2(3)} \\~\\ h = \frac{-44\pm278}{6} \\~\\ h=\frac{-44+278}{6}=39 \qquad\text{or}\qquad h=\frac{-44-278}{6}=-\frac{161}3$$

So...the height of the tree must be 39 feet

hectictar  May 13, 2017
#2
+75324
+2

Let the tree height  = h

And we have a rigrt triangle such that :

h^2  +  80^2   =  (2h + 11)^2     simplify

h^2  +  6400  =  4h^2 + 44h + 121

3h^2 + 44h  - 6279  = 0

Solving this  using  the  quadratic formula and taking the positive answer  we get that h =39 ft

CPhill  May 13, 2017

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