document.write( "Question 141297This question is from textbook Algebra 2
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\n" ); document.write( "A=42(angle A)
\n" ); document.write( "b=120 (side b)
\n" ); document.write( "c=160 (side c) \n" ); document.write( "
Algebra.Com's Answer #102942 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Solve the triangle using Law of sines or cosines.
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document.write( "Keep all decimals until the end, then round.\r\n" );
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document.write( "\"a%5E2=b%5E2%2Bc%5E2-2%2Ab%2Ac%2AcosA\"\r\n" );
document.write( "\"a%5E2=120%5E2%2B160%5E2-2%2A120%2A160%2Acos42\"°\r\n" );
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document.write( "Make sure your calculator is in DEGREE mode\r\n" );
document.write( "and not RADIAN mode.\r\n" );
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document.write( "Punch that in your calculator and you get:\r\n" );
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document.write( "\"a%5E2=11463.2387\"\r\n" );
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document.write( "Then taking square roots of both sides\r\n" );
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document.write( "\"a+=+107.0665153\"\r\n" );
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document.write( "Now we use the law of sines:\r\n" );
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document.write( "\"a%2FsinA=b%2FsinB=c%2FsinC\"\r\n" );
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document.write( "We need only the first two parts:\r\n" );
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document.write( "\"a%2FsinA=b%2FsinB\"\r\n" );
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document.write( "cross-multiply:\r\n" );
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document.write( "\"a%2AsinB+=+b%2AsinA\"\r\n" );
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document.write( "Divide both sides by a\r\n" );
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document.write( "\"sinB+=+%28b%2AsinA%29%2Fa\"\r\n" );
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document.write( "Substitute:\r\n" );
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document.write( "\"sinB+=+%28120%2Asin42%29%2F107.0665153\"\r\n" );
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document.write( "Calculate\r\n" );
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document.write( "\"sinB+=+0.7499606439\"\r\n" );
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document.write( "No use the inverse sine key \r\n" );
document.write( "on your calculator\r\n" );
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document.write( "\"B+=+48.58696886\"°\r\n" );
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document.write( "Now we find angle C from\r\n" );
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document.write( "\"A+%2B+B+%2B+C+=+180\"°\r\n" );
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document.write( "\"C+=+180+-+A+-+B\"\r\n" );
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document.write( "\"C+=+180+-+42+-+48.58696886\"\r\n" );
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document.write( "\"C+=+180+-+42+-+48.58696886\"\r\n" );
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document.write( "\"C+=+89.41303114\"°\r\n" );
document.write( "  \r\n" );
document.write( "So the three missing parts are\r\n" );
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document.write( "\"a+=+107.0665153\"\r\n" );
document.write( "\"B+=+48.58696886\"°\r\n" );
document.write( "\"C+=+89.41303114\"°\r\n" );
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document.write( "But using the rounding rules, the angles\r\n" );
document.write( "should be rounded to the nearest degree just \r\n" );
document.write( "like the given angle 42°, and the side should\r\n" );
document.write( "be rounded to the nearest two significant \r\n" );
document.write( "digits.  So using the rounding rules:\r\n" );
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document.write( "\"a+=+110\"  (side a)\r\n" );
document.write( "\"B+=+49\"°  (Angle B) \r\n" );
document.write( "\"C+=+89\"°  (Angle C)\r\n" );
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document.write( "Edwin
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