SOLUTION: I need help on setting up a question. It says a rope is stretched from the bottom of one pole to the top of the other pole. One pole is 8 feet tall and the other one is 24 feet tal

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Question 1011114: I need help on setting up a question. It says a rope is stretched from the bottom of one pole to the top of the other pole. One pole is 8 feet tall and the other one is 24 feet tall, and I need to find how far above the ground in which the ropes touch. I know that I need to set up a proportion, but I do not know enough information to set one up.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Thinking about this as a picture suggests a possible coordinate geometry solution using x y plane. Pick a value for the distance between the bottoms of the poles, like 10. Short pole is at the origin and long pole is 10 units to the right. Two lines are y=24x/10 for the bottom of the short to the top of the long pole; and y=-(8/10)x+8 for the bottom of the long pole to the top of the short pole.

These equations are system%28y=%2812%2F5%29x%2Cy=-%284%2F5%29x%2B8%29. Find the y coordinate for the intersection of these two lines. First equating the two formulas for y seems easiest, find x that way, and then evaluate the corresponding y value.

Result seems to be system%28x=2%261%2F2%2Chighlight%28y=6%29%29.

graph%28300%2C300%2C-2%2C12%2C-2%2C26%2C12x%2F5%2C-4x%2F5%2B8%29