document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142030>Question 1142030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Provide a sketch for this information.<BR>\n" );
document.write( "From a horizontal distance of 10.5km, a pilot observes that that the angles of depression of the top and base of a control tower are 36degrees and 41degrees respectively. Calculate height of the control tower </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762685 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=762685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's your sketch.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/060902.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "point A is the airplane.<BR>\n" );
document.write( "point F is the top of the tower.<BR>\n" );
document.write( "point C is the bottom of the tower.\r<BR>\n" );
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document.write( "AB is the horizontal distance from the plane to the tower at the level of the plane.\r<BR>\n" );
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document.write( "DC is the horizontal distance from the plane to the tower at the level of the bottom of the tower.\r<BR>\n" );
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document.write( "EF is the horizontal distance from the plane to the tower at the level of the top of the tower.\r<BR>\n" );
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document.write( "ABCD is the rectangle formed.\r<BR>\n" );
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document.write( "angle BAF is the angle of depression from the plane to the top of the tower.\r<BR>\n" );
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document.write( "angle BAC is the angle of depression from the plane to the bottom of the tower.\r<BR>\n" );
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document.write( "AF forms the diagonal of rectangle ABFE.\r<BR>\n" );
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document.write( "AC forms the diagonal of rectangle ABCD.\r<BR>\n" );
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document.write( "angle AFE is equal to angle BAF because they form alternate interior angles of parallel lines AB and EF.\r<BR>\n" );
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document.write( "angle ACD is equal to angle BAC because they form alternate interior angles of parallel lines AB and DC.\r<BR>\n" );
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document.write( "two triangles formed are triangles AFE and ACD.\r<BR>\n" );
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document.write( "the base of both of these triangles (EF and DC) are each 10.5 kilometers in length.\r<BR>\n" );
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document.write( "the length of BF is equal to y.\r<BR>\n" );
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document.write( "the length of FC is equal to x.\r<BR>\n" );
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document.write( "the length of BC is equal to x + y.\r<BR>\n" );
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document.write( "in triangle AFE, tangent of angle AFE is equal to y / 10.5.\r<BR>\n" );
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document.write( "in triangle ACD, tangent of angle ACD is equal to (x + y) / 10.5\r<BR>\n" );
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document.write( "since angle AFE is equal to 36 degrees, you get tan(36) = y / 10.5\r<BR>\n" );
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document.write( "since angle ACED is equal to 41 degrees, you get tan(41) = (x + y) / 10.5\r<BR>\n" );
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document.write( "solve for y in the first equation of tan(36) = y / 10.5 to get:\r<BR>\n" );
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document.write( "y = 10.5 * tan(36).\r<BR>\n" );
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document.write( "multiply both sides of the second equation of tan(41) = (x + y) / 10.5 to get:\r<BR>\n" );
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document.write( "10.5 * tan(41) = x + y\r<BR>\n" );
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document.write( "replace y with 10.5 * tan(36) to make that equation become:\r<BR>\n" );
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document.write( "10.5 * tan(41) = x + 10.5 * tan(36)\r<BR>\n" );
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document.write( "subtract 10.5 * tan(36) from both sides of that equation to get:\r<BR>\n" );
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document.write( "10.5 * tan(41) - 10.5 * tan(36) = x\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "y = 10.5 * tan(36).\r<BR>\n" );
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document.write( "x = 10.5 * tan(41) - 10.5 * tan(36)..\r<BR>\n" );
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document.write( "solve for each to get:\r<BR>\n" );
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document.write( "y = 7.628696544.\r<BR>\n" );
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document.write( "x = 1.498814203.\r<BR>\n" );
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document.write( "that makes x + y = 9.127510747.\r<BR>\n" );
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document.write( "the height of the tower is equal to x.\r<BR>\n" );
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document.write( "therefore, your solution is that the height of the tower is equal to 1.498814203 kilometers.\r<BR>\n" );
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document.write( "sounds awfully high for a tower, but that's what i get from my understanding of the information given.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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