document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28995>Question 28995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If i have a retangle with 20 in diagonal with 30 degree on on sid what is the lenght and width of that retangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15833 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=15833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If i have a retangle with 20 in diagonal with 30 degree on on sid what is the lenght and width of that retangle?\r<BR>\n" );
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document.write( "I am sorry I am not able to bring my diagram over to the answer box here.<BR>\n" );
document.write( "Please do as directed.<BR>\n" );
document.write( "Draw a rough sketch of a rectangle.Mark it ABCD,with A as the left hand bottom corner vertex and then naming in order the other three vertices in the anti-clockwise direction.<BR>\n" );
document.write( "Markdiagonal DB=20 and mark angle DBA = 30 degrees.<BR>\n" );
document.write( "Concentrate your attention on the right angled triangle DAB.<BR>\n" );
document.write( "Mark length AB = a and width AD =b<BR>\n" );
document.write( "We have angle DAB=90 degrees,the acute angle DBA = 30 degrees.<BR>\n" );
document.write( "and the hypotenuse DB=20<BR>\n" );
document.write( "Using Pytho Theorem,we have<BR>\n" );
document.write( " AB^2+DA^2= DB^2<BR>\n" );
document.write( "a^2+b^2=20^2<BR>\n" );
document.write( "a^2+b^2=400 ----(1)<BR>\n" );
document.write( "Applying the tangent funtion to the angle DBA  in this right angled triangle,<BR>\n" );
document.write( "we have tan(30)= opp side/adjac side <BR>\n" );
document.write( "1/[sqrt(3)] =(b/a)<BR>\n" );
document.write( "which gives   a =b[rt(3)]   ---=-(2)<BR>\n" );
document.write( "Using (2) in (1)<BR>\n" );
document.write( "a^2+b^2=400 <BR>\n" );
document.write( "{b[rt(3)]}^2 + b^2 = 400<BR>\n" );
document.write( "3b^2+b^2=400<BR>\n" );
document.write( "4b^2=400<BR>\n" );
document.write( "b^2=100 (dividing by 4)<BR>\n" );
document.write( "b= 10   <BR>\n" );
document.write( "(taking only the positive sqrt as we are talking about sides of a rectangle)<BR>\n" );
document.write( "Putting b=10 in (2),we have  a =b[rt(3)]= 10[sqrt(3)]<BR>\n" );
document.write( "Answer:Length of the rectangle =  10[sqrt(3)] and width = 10<BR>\n" );
document.write( "Verification: we should get (length)^2+(width)^2 = (diagonal)^2<BR>\n" );
document.write( "LHS= (length)^2+(width)^2 <BR>\n" );
document.write( "= {10[sqrt(3)]}^2 + 10^2 = (100X3) +100 = 400 = diagonal^2<BR>\n" );
document.write( "Therefore our values are correct.\r<BR>\n" );
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