# So there are 2 parallel lines 20 feet apart. A piece of pipe 20 feet long falls between the lines and one end is exactly 10 feet from one line. What is the probability that the pipe lies entirely between the lines?

Finding Geometric Probability
So there are 2 parallel lines 20 feet apart. A piece of pipe 20 feet long falls between the lines and one end is exactly 10 feet from one line. What is the probability that the pipe lies entirely between the lines?
I know how to do this if the pipes placement varies but not if it is fixed. Can anyone help me figure out the function and how I must integrate this?
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Kyan Hamilton
Step 1
You just need to compute the range of angles over which the pipe is inside the two libes and then divide by $2\pi$. It should be clear that thus the angular range is $\left[\mathrm{arccos}\left(1/2\right),\pi -\mathrm{arccos}\left(1/2\right)\right]$, or a range of $\pi -2\pi /3=\pi /3$.
Step 2
Thus the probability is, by symmetry, $\frac{2\pi /3}{2\pi }=\frac{1}{3}$.
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Ibrahim Rosales
Explanation:
Since one end of the pipe is 10 feet from one line. (I am assuming it is in between the two lines not outside. You can think of this also.) If the pipe is parallel to the lines then it's fine. Now start rotating the pipe, till it hits one end. Figure out the total angle during which it stays within the lines and $÷2\pi$.