document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148655>Question 148655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A trapezoid has two 65-degree angles and 9-inch and 12-inch parallel sides. How long are the non-parallel sides? What is the area enclosed by this figure? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109084 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=109084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's name the parallel sides as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=9inches ALIGN=MIDDLE  ALT=\"a%5B1%5D+=9inches\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=12inches ALIGN=MIDDLE  ALT=\"b%5B1%5D=12inches\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And the non parallel sides as \"c=?\" and \"d=?\".<BR>\n" );
document.write( "Before I proceed farther, I suggest you draw it on your own while we discuss it by words so you can follow better (just a suggestion).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now from that starting point and also the endpoint of that 9 inches which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, draw a line all the way down to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is perpendicular right? --> mark these lines as \"h\" (for height),likewise the 2 lines are parallel, and that line inside these parallel lines on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > also measures 9 inches right (of course) ---> mark it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now you have remaining length of 3 inches,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D-a%5B2%5D=12-9=3 ALIGN=MIDDLE  ALT=\"b%5B1%5D-a%5B2%5D=12-9=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And these 3 inches will be cut into half, 1-1/2\" on one side, likewise 1-1/2\" on the other. Why? Because you have opposite similar 65 deg angle right? (If not the same angle, the length won't be the same)<BR>\n" );
document.write( "The 1-1/2\" length mark one side as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D ALIGN=MIDDLE  ALT=\"b%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the other as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B3%5D ALIGN=MIDDLE  ALT=\"b%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Can you follow still?<BR>\n" );
document.write( "Now, side \"c\", \"h\" and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D ALIGN=MIDDLE  ALT=\"b%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > forms a right triangle (if you mark them properly) with angle 65 deg. To get \"c\",<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos65=b%5B2%5D%2Fc ALIGN=MIDDLE  ALT=\"cos65=b%5B2%5D%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=b%5B2%5D%2Fcos65 ALIGN=MIDDLE  ALT=\"c=b%5B2%5D%2Fcos65\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 1.5/cos65<BR>\n" );
document.write( "c=3.55 inches = d -------------> length of the non parallel sides<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For area in the trapezoid,<BR>\n" );
document.write( "A=1/2(h)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5B1%5D%2Bb%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28a%5B1%5D%2Bb%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To get \"h\", <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin65=h%2Fc ALIGN=MIDDLE  ALT=\"sin65=h%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h=(sin65)(3.55)=3.22 inches<BR>\n" );
document.write( "Therefore,<BR>\n" );
document.write( "A=(1/2)(3.22){9+12}<BR>\n" );
document.write( "A=33.81 sq inches<BR>\n" );
document.write( "<font><font size=4><b>Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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