document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190989>Question 1190989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a point on the floor the angle of elevation to the top of a door is 48 degrees, while the angle of elevation to the ceiling above the door is 56 degrees. If the ceiling is 10.5 feet above the floor, what is the vertical dimension of the door? Assume the floor and door form a right angle. (Round the the answer to one decimal place.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822745 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=822745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Here's the diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/MZOejbv.png\"><BR>\n" );
document.write( "This diagram (and the other one as well) is not to scale.\r<BR>\n" );
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document.write( "If you want, it might be beneficial to split the triangles up like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/74lChfm.png\"><BR>\n" );
document.write( "The goal is to find the value of y, i.e. the length of segment BD.\r<BR>\n" );
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document.write( "For now, focus on triangle ABC.<BR>\n" );
document.write( "We need to find x<BR>\n" );
document.write( "Use the tangent ratio<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(C) = AB/BC<BR>\n" );
document.write( "tan(56) = 10.5/x<BR>\n" );
document.write( "x*tan(56) = 10.5<BR>\n" );
document.write( "x = 10.5/tan(56)<BR>\n" );
document.write( "x = 7.082339 which is approximate\r<BR>\n" );
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document.write( "Now move to triangle BCD. Use that x value and the tangent ratio to find y<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(C) = BD/BC<BR>\n" );
document.write( "tan(48) = y/x<BR>\n" );
document.write( "y = x*tan(48)<BR>\n" );
document.write( "y = 7.082339*tan(48)<BR>\n" );
document.write( "y = 7.865734 this is also approximate\r<BR>\n" );
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document.write( "The last step is to round to the nearest tenth to get <font color=red>7.9 feet</font><BR>\n" );
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