document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076896>Question 1076896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The three angles of a triangle are 60 degrees, 76.67 degrees, 43.33 degrees respectively. If the area of the triangle is 88.33 square units find the length of the longest side of the triangle. What is the perimeter of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #691491 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=691491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The three angles of a triangle are 60 degrees, 76.67 degrees, 43.33 degrees respectively. If the area of the triangle is 88.33 square units find the length of the longest side of the triangle. What is the perimeter of the triangle? <BR>\n" );
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document.write( "Note:: The side opposite the 76.67 degree angle is the longest.<BR>\n" );
document.write( "Let that side be \"c\" ; let \"a\" be opposite 60 deg ; let \"b\" be opp 43.33<BR>\n" );
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document.write( "Formula: Area = a*b*sin(C)<BR>\n" );
document.write( "Solve for \"c\"::<BR>\n" );
document.write( "88.33 = a*c*sin(B) = 0.6862 ac<BR>\n" );
document.write( "88.33 = b*c*sin(A) = 0.8660 bc<BR>\n" );
document.write( "88.33 = a*b*sin(C) = 0.9731 ab<BR>\n" );
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document.write( "88.33/0.6862a = 88.33/0.8660b<BR>\n" );
document.write( "128.72/a = 102/b<BR>\n" );
document.write( "b = 102a/128.72<BR>\n" );
document.write( "b =  0.79a<BR>\n" );
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document.write( "So, 88.33 = 0.9731a(0.79a)<BR>\n" );
document.write( "88.33 = 0.7711a^2<BR>\n" );
document.write( "a = sqrt(114.55) = 10.7<BR>\n" );
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document.write( "Then c = 88.33/(0.6862*10.7) = 12.03<BR>\n" );
document.write( "And b = 88.33/(0.9731*10.7) = 8.48<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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