document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062546>Question 1062546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A workshop table has an equilateral triangular top, each side is 900mm, the legs being at the three corners. A load of 500N is placed on the table at a point distant 325mm from one leg and 625mm from another. What is the load in each of the three legs. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677521 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> height(h) of equilateral triangle: 900*sqrt(3)/2 = 450*sqrt(3)<BR>\n" );
document.write( "area of the equilateral triangle is sqrt(3)*900^2/4 = 202500*sqrt(3)<BR>\n" );
document.write( "Let the point at 325mm from one leg and 625mm from another be P.<BR>\n" );
document.write( "We draw three line segments from point P to each of the vertices of the equilateral triangle.<BR>\n" );
document.write( "Now, let V(1), V(2), V(3) be the vertices of the triangular table top, x be the length of a side, L(1), L(2), L(3) be the loads on the three legs.<BR>\n" );
document.write( "And V(1)P+V(2)P+V(3)P = x*sqrt(3)<BR>\n" );
document.write( "V(1)P = 900*sqrt(3)-325-625<BR>\n" );
document.write( "we have all three distances from P to the vertices<BR>\n" );
document.write( "we have three triangles to consider, (V(2),P,V(3)), (V(1),V(2),P) and (V(3),P,(V(1))<BR>\n" );
document.write( "select triangle (V(2),P,V(3)) to work with, the other two are done in a similar manner<BR>\n" );
document.write( "L(1) will be the load*ratio of the area of triangle (V(2),P,V(3)) to the area of (V(1),V(2),V(3)<BR>\n" );
document.write( "L(1) = 500*area of (V(2),P,V(3))/202500*sqrt(3)<BR>\n" );
document.write( "we can use Heron's formula to determine the area of triangle (V(2),P,V(3))<BR>\n" );
document.write( "T = sqrt(s(s-a)(s-b)(s-x)), where s = (a+b+x)/2, a=325, b=625, x=900<BR>\n" );
document.write( "Do L(2) and L(3) the same way. </SPAN>\n" );
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