document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139374>Question 139374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tell whether a triangle with the sides of the given lengths is 45°-45° -90°, 30° -60° -90° or neither.\r<BR>\n" );
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document.write( "11, 22, 19.1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101628 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, that sort of depends on how precise you want to be.  A triangle with sides of 11, 22, and 19.1 is very, very close to a 30°-60°-90° triangle.  That is because a 30°-60°-90° triangle with a hypotenuse of 22 has sides of 11 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11sqrt%283%29 ALIGN=MIDDLE  ALT=\"11sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  19.1 is pretty close to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11sqrt%283%29 ALIGN=MIDDLE  ALT=\"11sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but not exactly, and in fact the only way to express the length of the long leg of the given triangle exactly is to say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11sqrt%283%29 ALIGN=MIDDLE  ALT=\"11sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an irrational number and there is no exact decimal equivalent because there are no two integers p and q such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Fq=sqrt%283%29 ALIGN=MIDDLE  ALT=\"p%2Fq=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, a mathematician must answer this question: Neither, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19.1%3C%3E11sqrt%283%29 ALIGN=MIDDLE  ALT=\"19.1%3C%3E11sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Presuming that the triangle is a right triangle having sides of 11, 22, and 19.1, it would be approximately a 29.752°, 60.248°, 90° triangle.\r<BR>\n" );
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document.write( "A landscape architect laying out a triangular flower bed in your back yard would say: 30°-60°-90° because 19.1 is a precise enough measurement for the purpose.\r<BR>\n" );
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document.write( "On the other hand, a rocket scientist planning an earth to the moon trajectory would say Neither, because in this case 19.1 isn't nearly close enough to the true value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11sqrt%283%29 ALIGN=MIDDLE  ALT=\"11sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for this purpose.  That one-quarter of a degree error in angular measure here on earth means missing the moon by over 1000 miles at the end of the 240,000 mile trip. </SPAN>\n" );
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