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 #456448 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456448\">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.\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\r<BR>\n" );
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document.write( "The easiest method is to use the difference of angles formula. \r<BR>\n" );
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document.write( "sin (A – B) = Sin A Cos B – Cos A Sin B\r<BR>\n" );
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document.write( "sin (60 - 45) = Sin 60 Cos 45 – Cos 60 Sin 45\r<BR>\n" );
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document.write( "sin <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5Eo ALIGN=MIDDLE  ALT=\"15%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Sin 60 Cos 45 – Cos 60 Sin 45\r<BR>\n" );
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document.write( "Length of hypotenuse = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%28sqrt%286%29+%2B+sqrt%282%29%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%28sqrt%286%29+%2B+sqrt%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282sqrt%286%29+%2B+2sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%282sqrt%286%29+%2B+2sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in simplest radical form)\r<BR>\n" );
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document.write( "You can do the check!!\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
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