document.write( "Question 1167924: A rhombus has an area of 200 cm^2 and one of its interior angles is 110 degrees
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Algebra.Com's Answer #851643 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A rhombus has an area of 200 cm^2 and one of its interior angles is 110 degrees
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document.write( "Each rhombus has all its 4 sides of the same length.\r\n" );
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document.write( "Let x be the length of a side of this rhombus.\r\n" );
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document.write( "For any parallelogram, including rhombi, the area is half the product of the adjacent sides\r\n" );
document.write( "by the sine of angle between them.\r\n" );
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document.write( "So, for the area of our rhombus, we have this equation\r\n" );
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document.write( "    x*x*sin(110°) = 200,\r\n" );
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document.write( "or\r\n" );
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document.write( "    x^2*sin(110°) = 200.\r\n" );
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document.write( "Hence,  x =  =  = 14.5889 cm, approximately.\r\n" );
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document.write( "So, question (a) is answered.\r\n" );
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document.write( "To answer question (b), use the cosine law.  Notice that the angle of the rhombus opposite to its longest\r\n" );
document.write( "diagonal, is  110° (given).\r\n" );
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document.write( "So, the length of the longer diagonal is\r\n" );
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document.write( "     =  = 23.90105 cm, approximately.\r\n" );
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document.write( "Thus, question (b) is answered.\r\n" );
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document.write( "The altitude of the rhombus is its area 200 cm^2 divided by the side \r\n" );
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document.write( "    the altitude =  = 13.70905277  cm  (approximately).\r\n" );
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