document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205070>Question 1205070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCD is a square of side 4 cm. Equilateral triangles are constructed on the sides of the square.\r<BR>\n" );
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document.write( "Find the length of EH and the area of triangle EDH. \r<BR>\n" );
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document.write( "Any square has all four interior angles of 90 degrees each. <BR>\n" );
document.write( "Angle ADC = 90\r<BR>\n" );
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document.write( "Any equilateral triangle has each interior angle of 60 degrees.<BR>\n" );
document.write( "Angle EDA = angle CDH = 60\r<BR>\n" );
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document.write( "Focus on the angles around point D.<BR>\n" );
document.write( "They must add to 360 to do a full sweep or full rotation.<BR>\n" );
document.write( "(angleEDH) + (angleEDA) + (angleADC) + (angleCDH) = 360<BR>\n" );
document.write( "(x) + (60) + (90) + (60) = 360<BR>\n" );
document.write( "x + 210 = 360<BR>\n" );
document.write( "x = 360-210<BR>\n" );
document.write( "x = 150\r<BR>\n" );
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document.write( "Angle EDH = 150 degrees<BR>\n" );
document.write( "Sides ED and DH of triangle EDH are 4 cm each.\r<BR>\n" );
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document.write( "For triangle EDH we have the SAS (side angle side) case here, which means we can use the law of cosines to find the missing side.\r<BR>\n" );
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document.write( "d^2 = e^2 + h^2 - 2*e*h*cos(D)<BR>\n" );
document.write( "(EH)^2 = (DH)^2 + (ED)^2  - 2*DH*ED*cos(angle EDH)<BR>\n" );
document.write( "(EH)^2 = 4^2 + 4^2 - 2*4*4*cos(150)<BR>\n" );
document.write( "(EH)^2 = 59.712813 <BR>\n" );
document.write( "EH = sqrt(59.712813)<BR>\n" );
document.write( "EH = 7.727407\r<BR>\n" );
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document.write( "Segment EH is roughly 7.727 cm long. Round this value however needed or however your teacher instructs.<BR>\n" );
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