SOLUTION: A cable is run from the top of a tree to a stake located 4m away from the base of the tree. the length of the cable is 1m less than twice the height of the tree. find the length of
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Question 730805: A cable is run from the top of a tree to a stake located 4m away from the base of the tree. the length of the cable is 1m less than twice the height of the tree. find the length of the cable. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A cable is run from the top of a tree to a stake located 4m away from
the base of the tree.
the length of the cable is 1m less than twice the height of the tree.
find the length of the cable.
:
Let x = height of the tree
then
(2x-1) = length of the cable
:
Use pythag, a^2 + b^2 = c^2, where
a = 4
b = x
c = (2x-1)
4^2 + x^2 = (2x-1)^2
16 + x^2 = 4x^2 - 4x + 1
16 = 4x^2 - x^2 - 4x + 1
16 = 3x^2 - 4x + 1
0 = 3x^2 - 4x + 1 - 16
A quadratic equation
3x^2 - 4x - 15 = 0
Factors to
(3x + 5)(x - 3) = 0
the positive solution
x = 3 meters is the height of the tree
then
2(3) - 1 = 5 meters is the length of the cable
:
:
Check this 4^2 + 3^2 = 5^2
