document.write( "Question 93794: I have a square, divided up into 4 quadrants and need to know which quadrant a point lies in. I know the length of all 3 sides of the triangle (the edge of the square is 90', and the other two sides are lengths from 2 adjacent corners to the point, e.g. 48' and 63'). How do I best figure the angles of the triangle in order to calculate where the point lies, or is there another way to do this? \n" ); document.write( "

Algebra.Com's Answer #68350 by Edwin McCravy(20055) $\"\"$ $\"About$

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I have a square, divided up into 4 quadrants and need to know which quadrant a point lies in. I know the length of all 3 sides of the triangle (the edge of the square is 90', and the other two sides are lengths from 2 adjacent corners to the point, e.g. 48' and 63'). How do I best figure the angles of the triangle in order to calculate where the point lies, or is there another way to do this?
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document.write( "Let's suppose the given square and point P are like this: \r\n" );
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document.write( "You are asked to determine whether P is in the upper left,\r\n" );
document.write( "upper right, lower left, or lower right quadrants.\r\n" );
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document.write( "One way of course is to draw it accurately and see.  The above\r\n" );
document.write( "is drawn accurately. Here we can see that it is in the bottom \r\n" );
document.write( "left quadrant.  However, \"looking and seeing\" does not count. \r\n" );
document.write( "So we will have to calculate it.  Have you had the \"law of \r\n" );
document.write( "cosines\"?  It can be done with or without that law. I will \r\n" );
document.write( "assume you have studied that law.  If you haven't please post \r\n" );
document.write( "again telling me you have not had the law of cosines and I \r\n" );
document.write( "will show you the other way.\r\n" );
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document.write( "We can calculate angle BAP by the law of cosines:\r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( "Using the inverse cosine we get\r\n" );
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document.write( " = 41.85879221°\r\n" );
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document.write( "Now we draw altitude PQ.\r\n" );
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document.write( "  \r\n" );
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document.write( "All we need do now is calculate AQ and PQ\r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = 35.75'\r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = 32.03025913'\r\n" );
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document.write( "So we see that both AQ and PQ are less \r\n" );
document.write( "than 45' (half of 90') this shows that the\r\n" );
document.write( "point P is in the lower left quadrant.\r\n" );
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document.write( "If AQ were greater than 45' and PQ less than 45',\r\n" );
document.write( "then P would have been in the lower right quadrant.\r\n" );
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document.write( "If AQ were less than 45' and PQ were greater than 45',\r\n" );
document.write( "then P would have been in the upper left quadrant.\r\n" );
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document.write( "If both AQ and PQ were greater than 45', then P would\r\n" );
document.write( "have been in the upper right quadrant.\r\n" );
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document.write( "Edwin

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