document.write( "Question 34008: 
Solve this triangle, if possible: a=8.4 b=22.1 A=33ｰ46' \n" );
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Algebra.Com's Answer #20372 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
 
Solve this triangle: a=8.4 b=22.1 A=33ｰ46'\r\n" );
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document.write( "                 \r\n" );
document.write( "                 .C\r\n" );
document.write( "  b = 22.1   .    \\r\n" );
document.write( "         .         \a = 8.4\r\n" );
document.write( "     .              \\r\n" );
document.write( " A.   33ｰ46'         \B  \r\n" );
document.write( "  ｯｯｯｯｯｯｯｯｯｯｯｯｯｯｯｯｯｯｯｯ\r\n" );
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document.write( "This is the ambiguous case.  Sometimes there is no solution,\r\n" );
document.write( "sometimes there is one solution, and sometimes there are two solutions.\r\n" );
document.write( "There is no solution when a is too short to reach down to AB.\r\n" );
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document.write( "If the picture above shows one possible solution, here is another:\r\n" );
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document.write( "                 .C\r\n" );
document.write( "  b = 22.1   .  / \r\n" );
document.write( "         .     /a = 8.4\r\n" );
document.write( "     .        /     \r\n" );
document.write( " A.   33ｰ46' / B  \r\n" );
document.write( "  ｯｯｯｯｯｯｯｯｯｯｯ\r\n" );
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document.write( "The side a can slant right or left if it is long enough to reach \r\n" );
document.write( "down to AB.  Sometimes a is so long that it can only slant to the right,\r\n" );
document.write( "and if we slant it to the left it extends left of A, and not create a \r\n" );
document.write( "second solution.  That would be the case when there would be only one\r\n" );
document.write( "solution.  We don't yet know how many solutions, if any, we have.\r\n" );
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document.write( "In any case we use the law of sines:\r\n" );
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document.write( "    a       b       c\r\n" );
document.write( "   覧覧 = 覧覧 = 覧覧予r\n" );
document.write( "   sinA   sinB    sinC\r\n" );
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document.write( "We only need this part of the law of sines:\r\n" );
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document.write( "    a       b      \r\n" );
document.write( "   覧覧 = 覧覧 \r\n" );
document.write( "   sinA   sinB   \r\n" );
document.write( "    \r\n" );
document.write( "We solve for sinB\r\n" );
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document.write( "   aｷsinB = bｷsinA\r\n" );
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document.write( "Divide both sides by sinB\r\n" );
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document.write( "     sinB = bｷsinA/a\r\n" );
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document.write( "     sinB = (22.1)sin(33ｰ46')/8.4\r\n" );
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document.write( "     sinB = 1.4623151\r\n" );
document.write( "  \r\n" );
document.write( "Uh oh!  The sine of an angle cannot exceed 1; therefore\r\n" );
document.write( "there is no solution.  That means side a, which is 8.4,\r\n" );
document.write( "is too short to reach down to AB, and we cannot draw a \r\n" );
document.write( "triangle with those parts.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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