document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765370>Question 765370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a ship, the angle of elevation of a point A at the top of a cliff is 21 degrees after the ship has sailed 2500m directly toward the foot of the cliff, the angle of elevation of A is 47 degrees. Find the height of the cliff. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466111 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=466111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Point B is where the 21 degree angle of elevation was taken.<BR>\n" );
document.write( "Point C is where the 47 degree angle of elevation was taken.<BR>\n" );
document.write( "Point D is at the base of the cliff.<BR>\n" );
document.write( "You now have a large triangle ABD<BR>\n" );
document.write( "Two smaller triangles ABC and ACD<BR>\n" );
document.write( "Putting in angles: Angle BCA = 133 degrees,<BR>\n" );
document.write( "Angle BAC = 26 degrees<BR>\n" );
document.write( "Considering triangle ABC:<BR>\n" );
document.write( "a/Sin A = b/Sin B<BR>\n" );
document.write( "2500/sin(26) = b/Sin(21)<BR>\n" );
document.write( "Cross multiply.<BR>\n" );
document.write( "(2500 * sin(21))/sin(26) = b<BR>\n" );
document.write( "b (Side AC) = 2043.75m<BR>\n" );
document.write( "Considering triangle ACD<BR>\n" );
document.write( "This is right angled at D<BR>\n" );
document.write( "sin = Opposite/Hypotenuse.<BR>\n" );
document.write( "sin(47) = Opposite/2043.75<BR>\n" );
document.write( "Opposite = sin(47) * 2043.75<BR>\n" );
document.write( "Opposite = 1494.7m<BR>\n" );
document.write( "This is the height of the cliff.<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( ":-)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );