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Question 132215: This is a story problem. There are two poles, 10m and 15m high, and 25m apart on level ground. A wire goes from the top of each pole to the bottom of the other pole. How do you find a function that expresses the height of the intersection of the wires in terms of the heights of the two poles? I know how to find the height of the intersection by plotting coordinates and finding the intersection of the 2 lines based on their slopes. The height of the intersecting point is 6m. Can you help me find the function to solve it?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are two poles, 10m and 15m high, and 25m apart on level ground. A wire goes from the top of each pole to the bottom of the other pole. How do you find a function that expresses the height of the intersection of the wires in terms of the heights of the two poles? I know how to find the height of the intersection by plotting coordinates and finding the intersection of the 2 lines based on their slopes. The height of the intersecting point is 6m. Can you help me find the function to solve it?
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I think you have the right idea.
Let the 10m pole have end points (0,0) and (0,10)
Let the 15m pole have end points (25,0) and (25,15)
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Find the equation of the line thru (0,0) and (25,15)
y = (15/25x or y = (3/5)x
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Find the equation of the line thru (0,10) and (25,0)
slope = -10/25 = -2/5
y=intercept is 10
Equation is y = (-2/5)x+10
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find the intersection of:
y = (3/5)x and y = (-2/5)x+10
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Substitute to solve for "x":
3/5 x = -2/5x + 10
x = 10
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Substitute to solve for y:
y = (3/5)10 = 6
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Point of intersection is (10,6)
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Cheers,
Stan H.
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