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Topic: Problem with a square (Read 5624 times) |
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x2862
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Problem with a square
« on: Mar 24th, 2010, 2:48am » |
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I'm pretty good at coordinate geometry but this problem a friend gave me is stumping me. any ideas? Should I be using the law of cosines?
A square with a side of length x has a interior point of p. the location of point p is shuch that the distance to 3 corners of the square is 500, 300, and 400 feet measured in a clockwise direction.what is the length of the side of the square?
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| « Last Edit: Mar 24th, 2010, 3:03am by x2862 » |
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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You can solve it algebraically. There are two ways to put the three distances in the square (see attachment). Putting the origin at the left lower corner, you can pick an x-coordinate for P, and calculate the rest from there by solving
x = sqrt(32-a2) + sqrt(42-a2)
x = a + sqrt(52-(32-a2))
or for the second case
x = sqrt(42-b2) + sqrt(52-b2)
x = b + sqrt(32-(42-b2))
It doesn't give particularly nice answers though.
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| « Last Edit: Mar 24th, 2010, 4:46am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Aryabhatta
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Re: Problem with a square
« Reply #4 on: Mar 24th, 2010, 5:57pm » |
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on Mar 24th, 2010, 11:00am, towr wrote:| I don't see any way to use that. |
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Sorry about that, I posted that link without trying it myself. In any case, it is kind of related to the problem and some people might find it interesting.
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