document.write( "Question 1013894: The sides of a parallelogram ABCD are AB=424 mm and AD=348 mm. If angle ABC is 130 degrees:
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Algebra.Com's Answer #630407 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "The sides of a parallelogram ABCD are AB=424 mm and AD=348 mm. If angle ABC is 130 degrees:
\n" ); document.write( "A. Find the lengths of the long and short diagonals.
\n" ); document.write( "B. Find the area and perimeter of a parallelogram ABCD.
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document.write( "B. Let me start with the perimeter. It is \r\n" );
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document.write( "     P = 2*(424 + 348) mm = . . .   Please calculate it yourself.\r\n" );
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document.write( "   Now with the area. The area of a parallelogram (of any parallelogram) is\r\n" );
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document.write( "     S = , \r\n" );
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document.write( "   where a and b are measures of two its adjacent sides and  is the angle between them \r\n" );
document.write( "   (see the lesson Area of a parallelogram in this site).\r\n" );
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document.write( "   So in your case  S = 424*348*sin(130°) = 424*348*sin(180°-130°) = 424*348*sin(50°) = . . . Please calculate it yourself.\r\n" );
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document.write( "A. Now let us calculate the long diagonal of the parallelogram.\r\n" );
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document.write( "   Make a sketch of the parallelogram and its elements.\r\n" );
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document.write( "   Use the Cosines Law (see the lesson Proof of the Law of Cosines revisited in this site or everywhere else). \r\n" );
document.write( "   \r\n" );
document.write( "   It says that if you know the measures of two sides a and b of a triangle and the angle  between them\r\n" );
document.write( "   then the third side of the triangle is \r\n" );
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document.write( "    = .\r\n" );
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document.write( "   So in your case c =  = .\r\n" );
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document.write( "   Notice that I replaced the angle 130° by the supplementary angle 50° and changed the sign of cosines.\r\n" );
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document.write( "   Now calculate it yourself please.\r\n" );
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document.write( "   Next, let us calculate the short diagonal of the parallelogram.\r\n" );
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document.write( "   Make a sketch again. \r\n" );
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document.write( "   Use the same Law of Cosines. This time you have the same measures of the sides. The only difference is in that \r\n" );
document.write( "   the angle between the sides is not 130°. It is the supplementary angle 180° - 130° = 50°.\r\n" );
document.write( "   \r\n" );
document.write( "   Thus the formula for the third side in this case is \r\n" );
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document.write( "     c = .\r\n" );
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document.write( "   Please calculate it yourself.\r\n" );
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document.write( "   From my side, the problem is solved.\r\n" );
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