SOLUTION: two vertical poles have heights 4 m and 12 m a rope is stretched from the top of each pole to the bottom o fthe otehr how far above the ground do the ropes cross?

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Question 255408: two vertical poles have heights 4 m and 12 m a rope is stretched from the top of each pole to the bottom o fthe otehr how far above the ground do the ropes cross?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
picture the 4m pole standing at the origin, running up the y-axis

the 12m pole is standing on the x-axis, A meters away

the slope of the line from the bottom of 4m to the top of 12m is 12/A
___ the y-intercept is 0
___ the equation is y = 12x / A

the slope of the line from the top of 4m to the bottom of 12m is -4/A
___ the y-intercept is 4
___ the equation is y = -4x / A + 4

to find the intersection ___ 12x / A = -4x / A + 4 ___ 16x / A = 4 ___ 16x = 4A ___ 4x = A

substituting ___ y = 12x / 4x = 3

the height of the intersection is 3m