document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029872>Question 1029872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right triangle has a hypotenuse of length 37, and the lengths of both of its legs are integers. Find the sum of the sine of the smallest angle and the secant of the smallest angle of this right triangle. Express your answer as an improper fraction reduced to lowest terms.\r<BR>\n" );
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document.write( "Answer: 1789/1295\r<BR>\n" );
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document.write( "There must be some law that could explain this for me. Could you please help??\r<BR>\n" );
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document.write( "Thank you so much!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644794 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So in other words, the sum of the squares of the legs has to equal 37 using the Pythagorean theorem.<BR>\n" );
document.write( "There's only one pair, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2%2B35%5E2=37%5E2 ALIGN=MIDDLE  ALT=\"12%5E2%2B35%5E2=37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So then, the smallest angle of this triangle occurs where,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29=12%2F37 ALIGN=MIDDLE  ALT=\"sin%28theta%29=12%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29=35%2F37 ALIGN=MIDDLE  ALT=\"cos%28theta%29=35%2F37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29=37%2F35 ALIGN=MIDDLE  ALT=\"sec%28theta%29=37%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the sum is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=sin%28theta%29%2Bsec%28theta%29 ALIGN=MIDDLE  ALT=\"S=sin%28theta%29%2Bsec%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=12%2F37%2B37%2F35 ALIGN=MIDDLE  ALT=\"S=12%2F37%2B37%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=420%2F%2835%2A37%29%2B1369%2F%2835%2A37%29 ALIGN=MIDDLE  ALT=\"S=420%2F%2835%2A37%29%2B1369%2F%2835%2A37%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=1789%2F1295 ALIGN=MIDDLE  ALT=\"S=1789%2F1295\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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