SOLUTION: at a point on the ground 24ft from the base of a tree, the distance to the top of the tree if 4ft more than 3 times the height of the tree. Find the height of the tree.

Question 668529: at a point on the ground 24ft from the base of a tree, the distance to the top of the tree if 4ft more than 3 times the height of the tree. Find the height of the tree.
Found 2 solutions by jim_thompson5910, swincher4391:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let h = height of tree

If "at a point on the ground 24ft from the base of a tree, the distance to the top of the tree if 4ft more than 3 times the height of the tree", then the distance is 3h+4 (and this is the hypotenuse while the other two values are the legs of a right triangle)

Now use the Pythagorean theorem

a^2 + b^2 = c^2

24^2 + h^2 = (3h+4)^2

576 + h^2 = 9h^2 + 24h + 16

0 = 9h^2 + 24h + 16 - h^2 - 576

0 = 8h^2 + 24h - 560

8h^2 + 24h - 560 = 0

8(h^2 + 3h - 70) = 0

8(h+10)(h-7) = 0

h+10 = 0 or h-7 = 0

h = -10 or h = 7

Toss out the negative height (since it doesn't make sense) to get the only answer of h = 7

So the height of the tree is 7 ft.
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
If we were to draw a picture of a right triangle where the base is the distance from the point to the base of the tree, the height is the height of the tree and the distance from the point to the top of the tree is the hypotenuse, we can apply the Pythagorean THM:
Let a be the height of the tree.
Let b be the point to the base.
Let c be the point to the top.
a^2 + b^2 = c^2
a^2 + 24^2 = (3a+4)^2
a^2 + 576 = 9a^2 + 24a + 16
-8a^2 -24a + 560 = 0
-8(a^2+3a-70)
(a+10)(a-7)
So a = 7 or a = -10.
Height can't be negative, so we only accept the positive answer leaving us with a = 7 ft.
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