The question is as written: "Now given a rope hanging from the top of a pole. The end lying on the ground is 3 chi long. When tightly stretched it is 8 chi from the bottom of the pole. Let x represent the height of the pole. Tell: how long is the rope and how high is the pole?"
I am told to find the equation for the problem, but I am having difficulty making sense of the problem itself. What I have so far is this...
-The length of the pole is equal to x. -The length from the base of the pole to where the rope touches the ground when it is stretched out is equal to 8 chi.
-And the hypotenuse of the triangle is equal to x+3 as it is understood that if the rope is left alone, it is the length of the pole with 3 chi added to it.
What I have done so far is use the pythagorean theorem to get the equation: (x^2) + (8^2) = (x+3)^2 but after that is where I get lost in trying to find the equation or how to simplify this equation for the length of the rope. Any and all help is appreciated.