document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=757949>Question 757949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cathedral ceiling shown in the figure below is 8 feet high at the west wall of a room. As you go from the west wall toward the east wall, the ceiling slants upward. Three feet from the west wall, the ceiling is 10.5 feet high.<BR>\n" );
document.write( "What is the slope of the ceiling?<BR>\n" );
document.write( " The width of the room (the distance from the west wall to the east wall) is 17 feet. How high is the ceiling at the east wall?<BR>\n" );
document.write( "You want to install a light in the ceiling as far away from the west wall as possible. You intend to change the bulb, when required, by standing near the top of your stepladder. If you stand on the highest safe step of your stepladder, you can reach 21 feet high. How far from the west wall should you install the light?\r<BR>\n" );
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document.write( "I obviously need to find slope first , i tried using 10.5 as my run and 8 as my rise and a combination of others, if you can just help me find slope i think i can get the rest. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461407 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=461407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An intriguing problem.<BR>\n" );
document.write( "The slope of the ceiling.<BR>\n" );
document.write( "As the wall is 8ft high at the West wall<BR>\n" );
document.write( "then if 3ft from the West wall the ceiling has risen by <BR>\n" );
document.write( "2.5 ft (10.5 - 8) then using tan ratio<BR>\n" );
document.write( "Tan x = 2.5/3 = 39.8 degrees<BR>\n" );
document.write( "The height of the ceiling at the East wall<BR>\n" );
document.write( "Distance between West and East walls = 17ft<BR>\n" );
document.write( "Using the tan ratio again<BR>\n" );
document.write( "Tan = Opposite/Adjacent<BR>\n" );
document.write( "Tan 39.8 = Opposite/17 ft<BR>\n" );
document.write( "Opposite = tan 39.8 * 17 = 14.2ft<BR>\n" );
document.write( "Now you must add this to the height of the<BR>\n" );
document.write( "ceiling at the West wall. So height of East wall<BR>\n" );
document.write( "ceiling = 14.2 ft + 8 ft = 22.2ft.<BR>\n" );
document.write( "Installing a light as far as you can from <BR>\n" );
document.write( "West wall. With a limit of 21 foot stepladder.<BR>\n" );
document.write( "First you must take off the 8ft for the East wall<BR>\n" );
document.write( "leaving 13 ft.<BR>\n" );
document.write( "Back to tan ratio.<BR>\n" );
document.write( "tan 39.8 = 13/ adjacent<BR>\n" );
document.write( "(Adjacent is distance from West wall)<BR>\n" );
document.write( "Adjacent = 13/tan 39.8<BR>\n" );
document.write( "Adjacent = 15.6ft<BR>\n" );
document.write( "At 15.6 ft from the West wall you can use a 21 ft stepladder<BR>\n" );
document.write( "so this is where to fix the light.<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( ":-) </SPAN>\n" );
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