document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=611188>Question 611188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I can't solve this word problem involving right triangles:\r<BR>\n" );
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document.write( "\"A surveyor finds that from point A on the ground the angle of elevation to the top of a mountain is 23degrees. When he is at point B that is 1/4 mile closer to the base of the mountain, the angle of elevation is 43degrees. Assuming that the two points are on the same line, how high is the mountain?\"\r<BR>\n" );
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document.write( "I don't know how to go about this problem, so if you could, please show and explain the steps as well. I would really appreciate it and it will help me keep up with our lessons. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #384859 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=384859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are being asked to compare 2 right triangles, both<BR>\n" );
document.write( "of which have a side in common, which is the height.<BR>\n" );
document.write( "At the surveyor's 1st position, call his distance from <BR>\n" );
document.write( "the base of the mountain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles<BR>\n" );
document.write( "Call the height of the mountain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+23+%29+=+h%2Fd+ ALIGN=MIDDLE  ALT=\"+tan%28+23+%29+=+h%2Fd+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+43+%29+=+h%2F%28+d+-+.25+%29+ ALIGN=MIDDLE  ALT=\"+tan%28+43+%29+=+h%2F%28+d+-+.25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "On my calculator,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+23+%29+=+.42447+ ALIGN=MIDDLE  ALT=\"+tan%28+23+%29+=+.42447+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan%28+43+%29+=+.93252+ ALIGN=MIDDLE  ALT=\"+tan%28+43+%29+=+.93252+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.42447+=+h%2Fd+ ALIGN=MIDDLE  ALT=\"+.42447+=+h%2Fd+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+.42447d+ ALIGN=MIDDLE  ALT=\"+h+=+.42447d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.93252+=+h%2F%28+d+-+.25+%29+ ALIGN=MIDDLE  ALT=\"+.93252+=+h%2F%28+d+-+.25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+.93252d+-+.233130+ ALIGN=MIDDLE  ALT=\"+h+=+.93252d+-+.233130+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.42447d+=+.93252d+-+.233130+ ALIGN=MIDDLE  ALT=\"+.42447d+=+.93252d+-+.233130+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.93252d+-+.42447d+=+.233130+ ALIGN=MIDDLE  ALT=\"+.93252d+-+.42447d+=+.233130+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.50805d+=+.233130+ ALIGN=MIDDLE  ALT=\"+.50805d+=+.233130+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+.45887+ ALIGN=MIDDLE  ALT=\"+d+=+.45887+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+.42447d+ ALIGN=MIDDLE  ALT=\"+h+=+.42447d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+.42447%2A.45887+ ALIGN=MIDDLE  ALT=\"+h+=+.42447%2A.45887+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+.19478+ ALIGN=MIDDLE  ALT=\"+h+=+.19478+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The mountain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.19478+ ALIGN=MIDDLE  ALT=\"+.19478+\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles high, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.19478%2A5280+=+1028.42+ ALIGN=MIDDLE  ALT=\"+.19478%2A5280+=+1028.42+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft high<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+.42447d+ ALIGN=MIDDLE  ALT=\"+h+=+.42447d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.19478+=+.42447%2A.45887+ ALIGN=MIDDLE  ALT=\"+.19478+=+.42447%2A.45887+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.19478+=+.19478+ ALIGN=MIDDLE  ALT=\"+.19478+=+.19478+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.93252+=+h%2F%28+d+-+.25+%29+ ALIGN=MIDDLE  ALT=\"+.93252+=+h%2F%28+d+-+.25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.93252+=+.19478%2F%28+.45887+-+.25+%29+ ALIGN=MIDDLE  ALT=\"+.93252+=+.19478%2F%28+.45887+-+.25+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.93252+=+.19478%2F.20887+ ALIGN=MIDDLE  ALT=\"+.93252+=+.19478%2F.20887+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.93252+=+.93254+ ALIGN=MIDDLE  ALT=\"+.93252+=+.93254+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Error is due to rounding off </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );