document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42271>Question 42271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tower  stands vertically on sloping ground whose inclination with the  horizontal is 13 degrees. From a point 40.0m downhill from the  tower (measured along the  slope) the angle   of elevation of the top of the  tower is 20 degrees. How tall is  the  tower? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27426 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-10%2C45%2C-5%2C30%2C%0D%0Aline%280%2C0%2C39%2C0%29%2C%0D%0Aline%2839%2C0%2C39%2C25%29%2C%0D%0Aline%2839%2C9%2C0%2C0%29%2C%0D%0Aline%280%2C0%2C39%2C25%29%2C%0D%0Alocate%280%2C0%2CA%29%2C%0D%0Alocate%2839%2C0%2CB%29%2C%0D%0Alocate%2839%2C9%2CC%29%2C%0D%0Alocate%2839%2C25%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Let CD be the tower on the inclined plane AC.<BR>\n" );
document.write( "Inclination of AC with ground is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5Eo ALIGN=MIDDLE  ALT=\"13%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > is < BAC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5Eo ALIGN=MIDDLE  ALT=\"13%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Angle of elevation of the top of the tower is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5Eo ALIGN=MIDDLE  ALT=\"20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the point A which is at a distance of 40 m along the inclined plane from the base C of the tower.<BR>\n" );
document.write( "So < CAD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5Eo ALIGN=MIDDLE  ALT=\"20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and AC = 40 m.<BR>\n" );
document.write( "So < BAD = < BAC + < CAD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5Eo+%2B+20%5Eo ALIGN=MIDDLE  ALT=\"13%5Eo+%2B+20%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%5Eo ALIGN=MIDDLE  ALT=\"33%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In right-angled triangle ABC,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2FAC+=+cos%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"AB%2FAC+=+cos%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+AC%2Acos%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"AB+=+AC%2Acos%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+40%2Acos%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"AB+=+40%2Acos%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > _____(1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In right-angled triangle ABD,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD%2FAB+=+tan%2833%5Eo%29 ALIGN=MIDDLE  ALT=\"BD%2FAB+=+tan%2833%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD+=+AB%2Atan%2833%5Eo%29 ALIGN=MIDDLE  ALT=\"BD+=+AB%2Atan%2833%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD+=+40%2Acos%2813%5Eo%29%2Atan%2833%5Eo%29 ALIGN=MIDDLE  ALT=\"BD+=+40%2Acos%2813%5Eo%29%2Atan%2833%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [from (1)]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, in right-angled triangle ABD, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FAC+=+sin%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"BC%2FAC+=+sin%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+AC%2Asin%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"BC+=+AC%2Asin%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+40%2Asin%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"BC+=+40%2Asin%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Height of the tower = CD = BD - BC <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Acos%2813%5Eo%29%2Atan%2833%5Eo%29+-+40%2Asin%2813%5Eo%29 ALIGN=MIDDLE  ALT=\"40%2Acos%2813%5Eo%29%2Atan%2833%5Eo%29+-+40%2Asin%2813%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= 16.31\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence, the reqd. height of the mountain is 16.31 m. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );