document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288597>Question 288597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i  have a triangle with three angles of 45 75 and 60 degrees. the side opposite the 45 degrees is 5 long. how do i achieve the other two side please help. thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209180 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=209180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let your angles be A,B,C.\r<BR>\n" );
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document.write( "Let the sides opposite each of those angles be a,b,c.\r<BR>\n" );
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document.write( "Side a is opposite angle A.<BR>\n" );
document.write( "Side b is opposite angle B.<BR>\n" );
document.write( "Side c is opposite angle C.\r<BR>\n" );
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document.write( "angle A is equal to 45 degrees.<BR>\n" );
document.write( "angle B is equal to 75 degrees.<BR>\n" );
document.write( "angle C is equal to 60 degrees.\r<BR>\n" );
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document.write( "You are given that the side opposite the 45 degree angle is 5 units long.\r<BR>\n" );
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document.write( "Side a is 5 units long.\r<BR>\n" );
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document.write( "The law of Sines states that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28C%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the length of each side of a triangle is proportional to the measure of its corresponding angle.\r<BR>\n" );
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document.write( "In your triangle, this equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fsin%2845%29+=+b%2Fsin%2875%29+=+c%2Fsin%2860%29%7D%7D%0D%0A%0D%0A%0D%0AUse+your+calculator+to+find+the+sine+of+these+angles+and+then+substitute+in+the+equation+to+get%3A%0D%0A%0D%0A%0D%0A%7B%7B%7B5%2F.707106781+=+b%2F.965925826+=+c%2F.866025404 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F.707106781 ALIGN=MIDDLE  ALT=\"5%2F.707106781\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.071067812 ALIGN=MIDDLE  ALT=\"7.071067812\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F.965925826 ALIGN=MIDDLE  ALT=\"b%2F.965925826\"   DISABLED_style= \"max-width:90%; height:auto;\" > should be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.071067812 ALIGN=MIDDLE  ALT=\"7.071067812\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.965925826+%2A+7.071067812 ALIGN=MIDDLE  ALT=\".965925826+%2A+7.071067812\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.830127019 ALIGN=MIDDLE  ALT=\"6.830127019\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F.866025404 ALIGN=MIDDLE  ALT=\"c%2F.866025404\"   DISABLED_style= \"max-width:90%; height:auto;\" > should be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.071067812 ALIGN=MIDDLE  ALT=\"7.071067812\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.866025404+%2A+7.071067812 ALIGN=MIDDLE  ALT=\".866025404+%2A+7.071067812\"   DISABLED_style= \"max-width:90%; height:auto;\" > which equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.123724357 ALIGN=MIDDLE  ALT=\"6.123724357\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The sides of your triangle should be:\r<BR>\n" );
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document.write( "a = 5<BR>\n" );
document.write( "b = 6.830127019<BR>\n" );
document.write( "c = 6.123724357\r<BR>\n" );
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document.write( "The law of sines ratio should hold.\r<BR>\n" );
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document.write( "That ratio is, once again:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28c%29 ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In your equation, that becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fsin%2845%29+=+6.830127019%2Fsin%2875%29+=+6.123724357%2Fsin%2860%29 ALIGN=MIDDLE  ALT=\"5%2Fsin%2845%29+=+6.830127019%2Fsin%2875%29+=+6.123724357%2Fsin%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using the sines of those angles previously calculated gets us\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.071067812+=+7.071067812+=+7.071067812 ALIGN=MIDDLE  ALT=\"7.071067812+=+7.071067812+=+7.071067812\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The law of sines has held and your answer is:\r<BR>\n" );
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document.write( "a = 5<BR>\n" );
document.write( "b = 6.830127019<BR>\n" );
document.write( "c = 6.123724357<BR>\n" );
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