document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025720>Question 1025720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A woman standing on the top of a hill sees a flagpole that she knows is 14 meter tall. The angle of depression to the bottom of the pole is 7 degrees and the angle of elevation to the top of the pole is 35 degrees.\r<BR>\n" );
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document.write( "1. Find her distance from the flag pole.<BR>\n" );
document.write( "2. Given that the flag pole is placed on the same ground level as the hill and the woman is 1.73 meter tall. How high is the hill? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641021 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your diagram looks like this as far as i can tell.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/031902.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "from this diagram, you get:\r<BR>\n" );
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document.write( "tan(35) = x/y\r<BR>\n" );
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document.write( "tan(7) = (14-x)/y\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = x/tan(35) and y = (14-x)/tan(7)\r<BR>\n" );
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document.write( "this results in x/tan(35) = (14-x)/tan(7)\r<BR>\n" );
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document.write( "multiply both sides of this equation by tan(7) * tan(35) to get:\r<BR>\n" );
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document.write( "x*tan(7) = (14-x)*tan(35)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "x*tan(7) = 14*tan(35) - x*tan(35)\r<BR>\n" );
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document.write( "add x*tan(35) to both sides of this equation to get:\r<BR>\n" );
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document.write( "x*tan(7) + x*tan(35) = 14*tan(35)\r<BR>\n" );
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document.write( "factor out the x to get:\r<BR>\n" );
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document.write( "x*(tan(7) + tan(35)) = 14*tan(35)\r<BR>\n" );
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document.write( "divide both sides of this equation by (tan(7) + tan(35)) to get:\r<BR>\n" );
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document.write( "x = (14*tan(35)) / (tan(7) + tan(35)\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 11.91129969\r<BR>\n" );
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document.write( "14-x is therefore equal to 14 - 11.91129969 = 2.08870031\r<BR>\n" );
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document.write( "y = x/tan(35) results in y = 11.91129969/tan(35) which results in y = 17.01109891\r<BR>\n" );
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document.write( "y = (14-x)/tan(7) results in y = 2.08870031/tan(7) which results in y = 17.01109891.\r<BR>\n" );
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document.write( "value of y looks good either way.\r<BR>\n" );
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document.write( "looking at the diagram, we see that:\r<BR>\n" );
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document.write( "BC = x = 11.91129969\r<BR>\n" );
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document.write( "CD = 14 - x = 2.08870031\r<BR>\n" );
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document.write( "BD = the height of the flagpole = BC + CD = 14.\r<BR>\n" );
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document.write( "y = AC = the distance between the woman and the flagpole = 17.01109891.\r<BR>\n" );
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document.write( "AE = distance between the height of the woman and the ground = 14 - x = 2.08870031.\r<BR>\n" );
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document.write( "since the height of the woman is 1.73, then the hill she is standing on must be 2.08870031 - 1.73 = .3587003101.\r<BR>\n" );
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document.write( "looks like we have everything you need.\r<BR>\n" );
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document.write( "her distance to the flagpole is 17.01109891 meters.\r<BR>\n" );
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document.write( "the height of the hill is .3587003101 meters.\r<BR>\n" );
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document.write( "i double checked my results and i believe they are correct.\r<BR>\n" );
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document.write( "hopefully you agree after looking at what i did.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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