document.write( "Question 247568: Two side and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.
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Algebra.Com's Answer #180586 by Edwin McCravy(20059) $\"\"$ $\"About$

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Two side and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.
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document.write( "There is always exactly one solution when the given \r\n" );
document.write( "side that is opposite the given angle is longer than \r\n" );
document.write( "the other given side.\r\n" );
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document.write( "In this problem, the given side b is opposite given \r\n" );
document.write( "angle B and b is shorter than the other given side a, \r\n" );
document.write( "so we cannot tell immediately.\r\n" );
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document.write( "To find out we use the law of sines. If the sine of the \r\n" );
document.write( "unknown angle opposite the other given side turns\r\n" );
document.write( "out to be greater than 1, there is no solution.  If it is less\r\n" );
document.write( "than 1, there are two solutions, and in very rare cases when it\r\n" );
document.write( "comes out exactly equal to 1, there is one solution, and it is\r\n" );
document.write( "a right triangle.   \r\n" );
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document.write( "Using the law of sines:\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "Since this sine came out less than 1, \r\n" );
document.write( "there are 2 solutions.\r\n" );
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document.write( "There are two angles with this sine, \r\n" );
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document.write( "one is\r\n" );
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document.write( "A = 28.60889789°\r\n" );
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document.write( "and the other is its supplement\r\n" );
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document.write( "A = 180° - 28.60889789° = 151.3911021°\r\n" );
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document.write( "Here's the triangle with A = 28.60889789°\r\n" );
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document.write( "We'll solve it first.\r\n" );
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document.write( "We find angle C by adding A and B and subtracting from\r\n" );
document.write( "180°:\r\n" );
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document.write( "angle C = 180° - (20° + 28.60889789°) = 131.3911021°\r\n" );
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document.write( "We find side c by the law of sines:\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "Here's the triangle with A = 151.3911021°\r\n" );
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document.write( "  \r\n" );
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document.write( "Now we'll solve it:\r\n" );
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document.write( "We find angle C by adding A and B and subtracting from\r\n" );
document.write( "180°:\r\n" );
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document.write( "angle C = 180° - (20° + 151.3911021°) = 8.608897887°\r\n" );
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document.write( "We find side c by the law of sines:\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "Edwin

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