document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750137>Question 750137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am given a right triangle with angle measures of 15 and 75 degrees.  The side opposite the  15 degree angle is 2 units long.  The question asks me to calculate the exact length of the hypotenuse in radical form.\r<BR>\n" );
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document.write( "I doubled the 15 degree angle and created a 30-60-90 triangle so I know the new hypotenuse is twice the new short side, and that the common long side is root three times the short side.  I also have the Pythagorean relations for the two right triangles, so I have a system of equations, but my system resolves to an identity.  I need to introduce some new information.\r<BR>\n" );
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document.write( "Thanks,  John </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456406 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am given a right triangle with angle measures of 15 and 75 degrees.  The side opposite the  15 degree angle is 2 units long.  The question asks me to calculate the exact length of the hypotenuse in radical form.<BR>\n" );
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document.write( "c is the hypotenuse<BR>\n" );
document.write( "sin(15) = 2/c<BR>\n" );
document.write( "c = 2/sin(15)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Use the Half-Angle formula to get sin(15)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2815%29+=+%28sqr%282+-+sqr%283%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%2815%29+=+%28sqr%282+-+sqr%283%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+2%2F%28sqrt%282+-+sqr%283%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"c+=+2%2F%28sqrt%282+-+sqr%283%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+4%2F%28sqrt%282+-+sqr%283%29%29%29 ALIGN=MIDDLE  ALT=\"c+=+4%2F%28sqrt%282+-+sqr%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+16%2F%282+-+sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+16%2F%282+-+sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+16%2A%282+%2B+sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+16%2A%282+%2B+sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+4sqrt%282+%2B+sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"c+=+4sqrt%282+%2B+sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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