document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233387>Question 233387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that angleCAB = 48.6°. He also measures CA as 316 ft and CB as 527 ft. Find the distance between A and B. Round your answer to the nearest foot. (Note: angleABC is an acute angle.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172300 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=172300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Drop a line perpendicular to line AC and intersecting line AC at point D.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That forms 2 right triangles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First is triangle ACD and second is triangle BCD.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AC = 316 feet (given)<BR>\n" );
document.write( "BC = 527 feet (given)<BR>\n" );
document.write( "angle CAB = 48.6 degrees (given)<BR>\n" );
document.write( "angle CAD = 58.6 degrees also because it's the same angle.\r<BR>\n" );
document.write( "\n" );
document.write( "sin(CAD) = CD / AC <BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "sin(48.6) = CD / 316<BR>\n" );
document.write( "multiply both sides of this equation to get:<BR>\n" );
document.write( "316 * sin(48.6) = CD<BR>\n" );
document.write( "This makes CD = 237.035098\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We use the value of CD to get angle CBD\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin(CBD) = CD / 527<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "sin(CBD) = 237.035098/527 = .44978197<BR>\n" );
document.write( "This makes angle CBD = 26.72969621 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can now find AD and BD.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cos(CAD) = AD / AC<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "cos(48.6) = AD / 316<BR>\n" );
document.write( "multiply both sides of this equation by 316 to get:<BR>\n" );
document.write( "316 * cos(48.6) = AD<BR>\n" );
document.write( "This makes AD = 208.9745494 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cos(CBD) = BD / BC<BR>\n" );
document.write( "multiply both sides of this equation by BC to get:<BR>\n" );
document.write( "BC * cos(CBD) = BD<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "527 * cos(26.72969621) = BD<BR>\n" );
document.write( "This makes BD = 470.6859304 feet\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Total length of AB = AD + BD = 208.9745494 + 470.6859304 = 679.6584798 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );