document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192725>Question 192725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One angle of an isosceles triangle has measure 150*. If the area of the triangle is 9 cm ^2, what is the perimeter to three significant digits? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144712 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=144712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the  isosceles  triangle  with  one  angle  of  150 deg,  tells  us  that  the  vertex  angle  is  150,  side  angles  are  each  15  deg ,  for  a  total  of  180 deg  (150+15+15)\r<BR>\n" );
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document.write( "If  side  angle  was  150,  2*150=300,  oversize  for  triangle  (180 deg)\r<BR>\n" );
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document.write( "If  we  sketch  this  triangle,  and  include  an  altitude  h,  base  =(2b),  and  sides =a\r<BR>\n" );
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document.write( "we  can  figure  Area  =9(given) =  (1/2) base  *  height\r<BR>\n" );
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document.write( "9=(1/2) (2b) (h)\r<BR>\n" );
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document.write( "but  height  is  related  to  base  thru  150 deg  angle,  or  15 deg  angle.\r<BR>\n" );
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document.write( "from  sketch ( just  make  a  rough sketch,  obtuse  isosceles  triangle)  h/b = tan  15<BR>\n" );
document.write( "or  h=(tan15)(b)=.268(b),  substituting  into  Area  eqn\r<BR>\n" );
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document.write( "9=(1/2) (2b) (.268b)=.268 *b^2\r<BR>\n" );
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document.write( "dividing  both  sides  by  .268\r<BR>\n" );
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document.write( "9/.268 =b^2<BR>\n" );
document.write( "33.582=b^2\r<BR>\n" );
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document.write( "taking  sq  rt<BR>\n" );
document.write( "5.795  =b\r<BR>\n" );
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document.write( "but  h=.268b=.268*5.795=1.5529\r<BR>\n" );
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document.write( "last  side  a  can  be  found  from,  h/a =  sin 15,  or  a=h/sin15 =1.5529/.2588=6\r<BR>\n" );
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document.write( "sides  of  triangle  are  a,  a,  and  2b,  or  6,6,11.590<BR>\n" );
document.write( "per =  sum  of  sides  =  23.590  ANSWER\r<BR>\n" );
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document.write( "checking  area  ,  a=(1/2) (11.590) (1.5529) =9  ok\r<BR>\n" );
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document.write( "to  check  sides,  pythagorous  can  be  used,  6^2=1.5529^2 + 5.795^2=6^2  ok  </SPAN>\n" );
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