document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019262>Question 1019262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if triangles EFG and LNM are right triangles and they are also similar what is the measure of F, I know that angles E and L go together and angles F and N go together and that angles G and M go together it then says to let G=8 1/10 N=2 1/2 and M=16 1/5 what is the measure of angle F </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635494 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "my diagram of your triangles formed is shown below:\r<BR>\n" );
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document.write( "since the triangles are similar, then:\r<BR>\n" );
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document.write( "angle N = angle F.\r<BR>\n" );
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document.write( "angle L = angle E.\r<BR>\n" );
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document.write( "angle M = angle G\r<BR>\n" );
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document.write( "i'm assuming that angles M and G are the right angles of their respective triangles.\r<BR>\n" );
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document.write( "this makes sides EF and LN the hypotenuse of their respective triangles.\r<BR>\n" );
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document.write( "in triangle EFG, i'm assuming that side E is opposite angle E, side F is opposite angle F, side G is opposite angle G.\r<BR>\n" );
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document.write( "in triangle LNM, i'm assuming that side L is opposite angle L, side N is opposite angle N, side M is opposite angle M.\r<BR>\n" );
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document.write( "this is the normal way that sides and angles of triangles are related to each other.\r<BR>\n" );
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document.write( "you are given that side G = 8 and 1/2, side N = 2 and 1/2, side M = 16 and 1/5.\r<BR>\n" );
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document.write( "under this assumption, the diagram marks the length of each side given.\r<BR>\n" );
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document.write( "you are asked to find the measure of angle F.\r<BR>\n" );
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document.write( "since the triangle are similar, then the measure of angle F is equal to the measure of angle N.\r<BR>\n" );
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document.write( "the sine of angle N is equal to the side opposite angle N divided by the hypotenuse.\r<BR>\n" );
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document.write( "this would be side N divided by side M.\r<BR>\n" );
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document.write( "in the diagram, side N is shown as the line segment LM and side M is shown as the line segment LN.\r<BR>\n" );
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document.write( "since the measure of side N is eual to 2 and 1/2, and the measure of side M is equal to 16 and 1/5, and since side N is opposite angle N, and since side M is the hypotenuse of the triangle LNM, then:\r<BR>\n" );
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document.write( "sine of angle N = opposite / hypotenuse = side N / side M = (2 and 1/2) / (16 and 1/5).\r<BR>\n" );
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document.write( "use your calculator to find the sine of angle N is equal to .1543209877.\r<BR>\n" );
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document.write( "angle N is therefore equal to the arcsine of .1543209877.\r<BR>\n" );
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document.write( "that makes angle N equal to 8.877417897 degrees.\r<BR>\n" );
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document.write( "since angle F is equal to angle N, then angle F is equal to 8.77417897 degrees as well.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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