document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=541207>Question 541207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the area of a 30,60,90 triangle with a height of 4 inches and an unknown base?\r<BR>\n" );
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document.write( "P.S. the answer must be a radical number<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354105 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area = 1/2 * Base * Height<BR>\n" );
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document.write( "Height = 4 (given)<BR>\n" );
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document.write( "The triangle is a 30-60-90. (given)<BR>\n" );
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document.write( "The 30-60-90 triangle is a special triangle that most students have to learn to manipulate.<BR>\n" );
document.write( "The sides of the triangle have a well-known relationship.<BR>\n" );
document.write( "The side opposite the 30 degree angle is the short side. <BR>\n" );
document.write( "The side opposite the 90 degree angle is the hypotenuse. It is twice the length of the short side.<BR>\n" );
document.write( "Applying the Pythagorean Theorem, we can calculate the third side. It will have a sqrt(3) component.<BR>\n" );
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document.write( "The relationships can be used to define the lengths of the sides.<BR>\n" );
document.write( "Let's call the short side S for \"short\".<BR>\n" );
document.write( "Call the hypotenuse H.<BR>\n" );
document.write( "Call the third side L for \"long\" because it is longer than S. Of course, it is shorter than H.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+S+=+%281%2F2%29%2AH+ ALIGN=MIDDLE  ALT=\"+S+=+%281%2F2%29%2AH+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+%281%2F2%29%2AH%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"+L+=+%281%2F2%29%2AH%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, we can determine:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L+=+S+%2A+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+L+=+S+%2A+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In what may be a typical layout, the L side is shown vertically, which makes it the height.<BR>\n" );
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document.write( "From the last equation (above), we can deduce that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+S+=+L+%2F+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+S+=+L+%2F+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That means:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Area+=+%281%2F2%29+%2A+%28L%2Fsqrt%283%29%29+%2A+L+ ALIGN=MIDDLE  ALT=\"+Area+=+%281%2F2%29+%2A+%28L%2Fsqrt%283%29%29+%2A+L+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Area+=+%281%2F2%29+%2A+%284%2Fsqrt%283%29%29+%2A+4+ ALIGN=MIDDLE  ALT=\"+Area+=+%281%2F2%29+%2A+%284%2Fsqrt%283%29%29+%2A+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Area+=+%281%2A4%2A4%29%2F%282%2Asqrt%283%29%29+ ALIGN=MIDDLE  ALT=\"+Area+=+%281%2A4%2A4%29%2F%282%2Asqrt%283%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Area+=+8%2Fsqrt%283%29+ ALIGN=MIDDLE  ALT=\"+Area+=+8%2Fsqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Done. </SPAN>\n" );
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