Question 764714: A Christmas tree is supported by a wire that is 1 foot longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 49 feet shorter than the height of the tree. what is the height of the tree?
Answer by dkrall(2)   (Show Source):
You can put this solution on YOUR website! Use Pythagorean theorem x^2+y^2=r^2, where y =(distance from base), x= (hight of tree) and r= (length of wire supporting the tree and solve for x.
The wire(r) is 1 foot longer than the hight(y), so r=(y+1). The distance from the anchor and the base of the tree is 49 feet shorter than the hight. So x=(y-49)
Which equals (x-49)^2+x^2=(x+1)^2. Now solve for x.
(x-49)^2+x^2=(x+1)^1 Which can then be factored as:
x^2+(x-49)(x-49)=(x+1)(x+1)
2x^2-98x+2401=x^2+2x+1
Combine terms:
x^2-100x+2400=0, Which comes out to be: (x-60)(x-40)=0
So x=60 or x=40. Test each x value (hight) to determine which one works, so base(y)= (60-49) ect..
Since 40 would make the base a negative number, x can only equal 60.
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