document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628648>Question 628648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 17°31'. When the boat stops, the angle of depression is 46°41'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395791 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=395791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person is watching a boat from the top of a lighthouse. <BR>\n" );
document.write( "The boat is approaching the lighthouse directly. <BR>\n" );
document.write( "When first noticed the angle of depression to the boat is 17°31'. <BR>\n" );
document.write( "When the boat stops, the angle of depression is 46°41'. <BR>\n" );
document.write( "The lighthouse is 200 feet tall. <BR>\n" );
document.write( "How far did the boat travel from when it was first noticed until it stopped?<BR>\n" );
document.write( " Round your answer to the hundredths place.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change 17 degrees 31 minutes to 17 + 31/60 = 17.5167 degrees<BR>\n" );
document.write( "Change 46 degrees 41 minutes to 46.6833 degrees<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can solve this using two right triangles<BR>\n" );
document.write( "90 - 17.5167 = 72.4833<BR>\n" );
document.write( "Side opposite will be distance (D) from the lighthouse to the boat when noticed<BR>\n" );
document.write( "Side adjacent: the lighthouse; 200 ft<BR>\n" );
document.write( "tan(72.4833) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2F200 ALIGN=MIDDLE  ALT=\"D%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D = 3.16837 * 200<BR>\n" );
document.write( "D = 633.675 ft, lighthouse to boat when noticed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The 2nd right triangle: <BR>\n" );
document.write( "90 - 46.6833 = 43.3167<BR>\n" );
document.write( "side opposite will be distance (d) from lighthouse to boat when it stopped<BR>\n" );
document.write( "tan(43.3167) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F200 ALIGN=MIDDLE  ALT=\"d%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = .9429 * 200<BR>\n" );
document.write( "d = 188.580 ft, lighthouse to boat it stopped<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Boat traveled: 633.675 - 188.580 = 445.09 ft </SPAN>\n" );
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