document.write( "Question 1029345: A rhombus of side 12 cm has two angles of 60 degree. Calculate the lengths of the diagonals of the rhombus. \n" ); document.write( "

Algebra.Com's Answer #644385 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "A rhombus of side 12 cm has two angles of 60 degree. Calculate the lengths of the diagonals of the rhombus.
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\n" ); document.write( "\n" ); document.write( "Apply the Law of Cosines.\r
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document.write( "The shorter diagonal\r\n" );
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document.write( "We work with the isosceles acute triangle whose lateral sides are 12 cm long and the angle between them is 60°.\r\n" );
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document.write( " =  =  =  = 12 cm.\r\n" );
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document.write( "As you see, the shorter diagonal has the length of 12 cm, same as the two other sides of this triangle,\r\n" );
document.write( "so the triangle is equilateral, actually.\r\n" );
document.write( "We could foresee it, since the isosceles triangle with one (any) angle of 60° is equiangular and equilateral.\r\n" );
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document.write( "The longer diagonal\r\n" );
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document.write( "We work with the isosceles obtuse triangle whose lateral sides are 12 cm long and the angle between them is 120°.\r\n" );
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document.write( " =  =  =  =  =  cm.\r\n" );
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document.write( "Answer.  The diagonals of the rhombus are  12 cm  and   cm.\r\n" );
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