document.write( "Question 450961: find the area of a parallelogram with diagonals of lengths 10 inches and 22 inches that intersect at a 65 degrees angle \n" ); document.write( "
Algebra.Com's Answer #310148 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Since the diagonals of a parallelogram bisect each other,\r\n" );
document.write( "and the diagonals are 10 and 22, then the halves of the\r\n" );
document.write( "diagonals are 5 and 11 \r\n" );
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document.write( "Look at the red triangle:\r\n" );
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document.write( "The interior angle at the top of the red triangle is\r\n" );
document.write( "supplementary to the 65° angle.  So it is 180°-65°=115°\r\n" );
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document.write( "We have a case of SAS, so we use the law of cosines to\r\n" );
document.write( "calculate b, the base of the red triangle:\r\n" );
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document.write( "bē = 11ē + 5ē - 2(11)(5)cos(115°)\r\n" );
document.write( "bē = 121 + 25 - 110(-.4226182617)\r\n" );
document.write( "bē = 285.4640264\r\n" );
document.write( " b = 16.8956807 inches.\r\n" );
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document.write( "We have the base of the parallelogram.\r\n" );
document.write( "Now we have to find the height of the parallelogram.\r\n" );
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document.write( "We will use the law of sines to find the angle Ꮎ\r\n" );
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document.write( "   5        b\r\n" );
document.write( " ————— = —————————\r\n" );
document.write( " sinᎾ    sin(115°)\r\n" );
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document.write( "b*sinᎾ  = 5sin(115°)\r\n" );
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document.write( "         5sin(115°)\r\n" );
document.write( " sinᎾ  = ———————————\r\n" );
document.write( "             b\r\n" );
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document.write( "         5sin(115°)\r\n" );
document.write( " sinᎾ  = ———————————\r\n" );
document.write( "         16.8956807\r\n" );
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document.write( " sinᎾ  = .2682069468\r\n" );
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document.write( "    Ꮎ  = 15.55759756°\r\n" );
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document.write( "Now we will extend the base and draw in the height \r\n" );
document.write( "of the parallelogram, labeling it h:\r\n" );
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document.write( "The big right triangle that has angle Ꮎ  on the left, and\r\n" );
document.write( "the opposide side h on the right, has a hypotenuse which\r\n" );
document.write( "is the longer diagonal, 22, so\r\n" );
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document.write( "         h\r\n" );
document.write( "sinᎾ  = —————\r\n" );
document.write( "        22\r\n" );
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document.write( "   h = 22(sinᎾ)\r\n" );
document.write( "   h = 22(.2682069468)\r\n" );
document.write( "   h = 5.90055283\r\n" );
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document.write( "Finally we can calculate the area of the parallelogram,\r\n" );
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document.write( "   A = bh\r\n" );
document.write( "   A = (16.8956807in)(5.90055283in)\r\n" );
document.write( "   A = 99.69385657 square inches\r\n" );
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document.write( "Edwin
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