document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043572>Question 1043572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A ship leaves a port and sails for 4 hours on a course of 78° at 18 knots. Then the ship changes it's course to 128° and sails for 6 hours at 16 knots. Find 10 hours after leaving the port:<BR>\n" );
document.write( "*the distance of ship from the part<BR>\n" );
document.write( "*the bearing of the ship from the port<BR>\n" );
document.write( "*the bearing from the ship to the port.\r<BR>\n" );
document.write( "\n" );
document.write( "2. A ship is sailing due west when a light is observed with heading 297°50' from the ship. After the ship has travelled 2250 feet, the light heads 311°55' from the ship. If the course is continued, how close will the ship approach the light?\r<BR>\n" );
document.write( "\n" );
document.write( "Please provide illustrations so I could study it. 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 #659159 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. I had to look up the definition of course, heading, and bearing,<BR>\n" );
document.write( "and what I found is some confusion.<BR>\n" );
document.write( "In most sources They were defined as the angle from North to the direction the ship is aiming for, or pointing to,<BR>\n" );
document.write( "measured clockwise from North.<BR>\n" );
document.write( "I am sticking to that, but I believe that for the first problem, it does not matter how you measure the angle, as long as it is done consistently.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284hours%29%2A%2818knots%29=72 ALIGN=MIDDLE  ALT=\"%284hours%29%2A%2818knots%29=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nautical ALIGN=MIDDLE  ALT=\"nautical\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=miles ALIGN=MIDDLE  ALT=\"miles\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286hours%29%2A%2816knots%29=96 ALIGN=MIDDLE  ALT=\"%286hours%29%2A%2816knots%29=96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nautical ALIGN=MIDDLE  ALT=\"nautical\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=miles ALIGN=MIDDLE  ALT=\"miles\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The situation can be sketched like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28660%2C300%2C-10%2C155%2C-50%2C25%2C%0D%0Alocate%28-9%2C2%2Cport%29%2Ccircle%280%2C0%2C1%29%2C%0D%0Atriangle%280%2C0%2C70.43%2C14.97%2C0%2C14.97%29%2Ctriangle%280%2C0%2C70.43%2C14.97%2C70.43%2C0%29%2C%0D%0Atriangle%2870.43%2C14.97%2C146.08%2C-44.13%2C146.08%2C14.97%29%2C%0D%0Atriangle%280%2C0%2C146.08%2C-44.13%2C146.08%2C0%29%2C%0D%0Ablue%28arrow%280%2C-20%2C0%2C22%29%29%2Cblue%28arrow%2870.42%2C-19%2C70.42%2C25%29%29%2C%0D%0Alocate%280%2C25%2Cblue%28N%29%29%2Clocate%2872%2C25%2Cblue%28N%29%29%2C%0D%0Ared%28line%280%2C0%2C70.43%2C14.97%29%29%2Cgreen%28line%28146.08%2C-44.13%2C70.43%2C14.97%29%29%2C%0D%0Arectangle%280%2C14.97%2C2%2C12.97%29%2Crectangle%2870.43%2C0%2C68.43%2C2%29%2C%0D%0Arectangle%28146.08%2C14.97%2C144.08%2C12.97%29%2Crectangle%28146.08%2C0%2C144.08%2C-2%29%2C%0D%0Agreen%28arc%2870.43%2C14.97%2C10%2C10%2C-90%2C38%29%29%2Clocate%2875.43%2C20.97%2Cgreen%28128%5Eo%29%29%2C%0D%0Ared%28arc%280%2C0%2C10%2C10%2C-90%2C-12%29%29%2Clocate%282%2C9.6%2Cred%2878%5Eo%29%29%2C%0D%0Alocate%2835.2%2C7.48%2Cred%2872%29%29%2Clocate%28108.25%2C-17%2Cgreen%2896%29%29%2C%0D%0Alocate%2833%2C18.5%2Cx%5B1%5D%29%2Clocate%28108.2%2C18.5%2Cx%5B2%5D%29%2C%0D%0Alocate%28142%2C12%2Cy%5B1%5D%29%2Clocate%28150%2C-10%2Cy%5B2%5D%29%2C%0D%0Aarrow%28149%2C-14.58%2C149%2C14.97%29%2Carrow%28149%2C-14.58%2C149%2C-44.13%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The right triangles with a red hypotenuse of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%2872%29 ALIGN=MIDDLE  ALT=\"red%2872%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > have legs measuring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=72%2Asin%2878%5Eo%29=70.42663 ALIGN=MIDDLE  ALT=\"x%5B1%5D=72%2Asin%2878%5Eo%29=70.42663\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to 5 decimal places) and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=72%2Acos%2878%5Eo%29=14.96964 ALIGN=MIDDLE  ALT=\"y%5B1%5D=72%2Acos%2878%5Eo%29=14.96964\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to 5 decimal places) .<BR>\n" );
document.write( "At <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours the ship was about 70 nautical miles East, and 15 miles North of the port.<BR>\n" );
document.write( "The legs of the right triangles with a green hypotenuse of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%2896%29 ALIGN=MIDDLE  ALT=\"green%2896%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=96%2Asin%28128%5Eo%29=75.64903 ALIGN=MIDDLE  ALT=\"x%5B2%5D=96%2Asin%28128%5Eo%29=75.64903\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to 5 decimal places) and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5B2%5D=96%2Acos%28128%5Eo%29=-59.1035 ALIGN=MIDDLE  ALT=\"-y%5B2%5D=96%2Acos%28128%5Eo%29=-59.1035\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to 5 decimal places) .<BR>\n" );
document.write( "After <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B6=10 ALIGN=MIDDLE  ALT=\"4%2B6=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours the ship was about 76 nautical miles further East, and 59 miles South from its position at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Considering only the start and end positions, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28660%2C300%2C-10%2C155%2C-59%2C16%2C%0D%0Alocate%28-9%2C2%2Cport%29%2Ccircle%280%2C0%2C1%29%2C%0D%0Atriangle%280%2C0%2C146.08%2C-44.13%2C146.08%2C0%29%2C%0D%0Ablue%28arrow%280%2C-27%2C0%2C13%29%29%2Cblue%28arrow%2870.42%2C-29%2C70.42%2C15%29%29%2C%0D%0Alocate%281%2C16%2Cblue%28N%29%29%2Clocate%2872%2C15%2Cblue%28N%29%29%2C%0D%0Arectangle%2870.43%2C0%2C68.43%2C2%29%2C%0D%0Aarrow%28146.08%2C0%2C146.08%2C14.97%29%2Carrow%28146.08%2C14.97%2C146.08%2C0%29%2C%0D%0Arectangle%28146.08%2C0%2C144.08%2C-2%29%2Ccircle%28146.08%2C-44.13%2C1%29%2C%0D%0Alocate%28147%2C-44%2Cend%29%2Clocate%28135%2C-20%2Cy%5B2%5D-y%5B1%5D%29%2C%0D%0Alocate%2833%2C3%2Cx%5B1%5D%29%2Clocate%28108.2%2C3%2Cx%5B2%5D%29%2C%0D%0Alocate%28142%2C12%2Cy%5B1%5D%29%2Clocate%28150%2C-10%2Cy%5B2%5D%29%2C%0D%0Aarrow%28149%2C-14.58%2C149%2C14.97%29%2Carrow%28149%2C-14.58%2C149%2C-44.13%29%2C%0D%0Aarrow%2873%2C-46%2C0%2C-46%29%2Carrow%2873%2C-46%2C146.08%2C-46%29%2C%0D%0Alocate%2865%2C-38%2Cx%5B1%5D%2Bx%5B2%5D%29%2Crectangle%280%2C0%2C2%2C2%29%2C%0D%0Ared%28arc%280%2C0%2C20%2C20%2C-90%2C16.8%29%29%2Cred%28arc%28146.08%2C-44.13%2C20%2C20%2C-90%2C196.8%29%29%2C%0D%0Aarc%280%2C0%2C30%2C30%2C0%2C16.8%29%2Clocate%2815%2C-1%2Ctheta%29%2C%0D%0Alocate%2810%2C8%2Cred%2890%5Eo%2Btheta%29%29%2Clocate%28140%2C-53%2Cred%28270%5Eo%2Btheta%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We have one right triangle, and we know the legs, so we can find<BR>\n" );
document.write( "the hypotenuse, and<BR>\n" );
document.write( "angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The lengths of the legs are approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D=70.42663%2B75.64903=146.07566 ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D=70.42663%2B75.64903=146.07566\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D-y%5B1%5D=59.10350-14.96964=44.13386%7D%7D%0D%0Aso+the+hypotenuse%2C+which+is+the+distance+from+the+ship+to+port+at+10+hours%2C+is+approximately%0D%0A%7B%7B%7Bsqrt%28144.07566%5E2%2B44.13386%5E2%29=highlight%28152.5972%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=44.13386%2F144.07566=0.30201 ALIGN=MIDDLE  ALT=\"tan%28theta%29=44.13386%2F144.07566=0.30201\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=163.8%5Eo ALIGN=MIDDLE  ALT=\"theta=163.8%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "the distance to the ship from the port is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28152.6%29 ALIGN=MIDDLE  ALT=\"highlight%28152.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > nautical miles,<BR>\n" );
document.write( "the bearing of the ship from the port is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo%2B16.8%5Eo=highlight%28106.8%5Eo%29 ALIGN=MIDDLE  ALT=\"90%5Eo%2B16.8%5Eo=highlight%28106.8%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "the bearing from the ship to the port is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%5Eo%2B16.8%5Eo=highlight%28286.8%5Eo%29 ALIGN=MIDDLE  ALT=\"270%5Eo%2B16.8%5Eo=highlight%28286.8%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. The ship is going West.<BR>\n" );
document.write( "When the ship reaches point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > it records the bearing/heading of the light,<BR>\n" );
document.write( "and it does it again, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2250 ALIGN=MIDDLE  ALT=\"2250\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet further, at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If the course is continued, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet further, the ship will reach point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "where it is at a distance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet from the light,<BR>\n" );
document.write( "as close to the light as its westward trajectory would take it.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28650%2C390%2C-300%2C6200%2C-850%2C3050%2C%0D%0Atriangle%280%2C0%2C0%2C2884.1%2C3215.5%2C0%29%2Crectangle%280%2C0%2C100%2C100%29%2C%0D%0Atriangle%280%2C0%2C0%2C2884.1%2C5462.5%2C0%29%2Carrow%28700%2C0%2C-300%2C0%29%2C%0D%0Ablue%28arrow%285462.5%2C-250%2C5462.5%2C3000%29%29%2Clocate%28-100%2C3000%2CL%29%2C%0D%0Acircle%280%2C0%2C30%29%2Ccircle%283212.5%2C0%2C30%29%2Ccircle%285462.5%2C0%2C30%29%2C%0D%0Alocate%285480%2C0%2CA%29%2Clocate%283230%2C0%2CB%29%2Clocate%2820%2C0%2CC%29%2C%0D%0Alocate%284700%2C250%2Cred%28311%5Eo%29%29%2Clocate%285050%2C170%2Cred%28%2255+%27%22%29%29%2C%0D%0Ared%28arc%285462.5%2C0%2C1550%2C1550%2C-90%2C207.8%29%29%2Cred%28line%280%2C2884.1%2C5462.5%2C0%29%29%2C%0D%0Ablue%28arrow%285462.5%2C-250%2C5462.5%2C3000%29%29%2Cblue%28arrow%283212.5%2C-250%2C3212.5%2C3000%29%29%2C%0D%0Alocate%282450%2C250%2Cgreen%28297%5Eo%29%29%2Clocate%282800%2C170%2Cgreen%28%2250+%27%22%29%29%2C%0D%0Agreen%28arc%283212.5%2C0%2C1550%2C1550%2C-90%2C222%29%29%2Cgreen%28line%280%2C2884.1%2C3212.5%2C0%29%29%2C%0D%0Alocate%2820%2C1550%2Cd%29%2Clocate%281400%2C0%2Cx%29%2Clocate%284000%2C0%2C2250%29%2C%0D%0Aarrow%285462.5%2C0%2C6500%2C0%29%2Clocate%283300%2C3050%2Cblue%28N%29%29%2C%0D%0Alocate%285550%2C3050%2Cblue%28N%29%29%2Clocate%28-300%2C-50%2CWEST%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We have two right triangles: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ALC ALIGN=MIDDLE  ALT=\"ALC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BLC ALIGN=MIDDLE  ALT=\"BLC\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ALC ALIGN=MIDDLE  ALT=\"ALC\"   DISABLED_style= \"max-width:90%; height:auto;\" > , a leg measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet is opposed to an angle measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=297%5Eo ALIGN=MIDDLE  ALT=\"297%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2250+%27%22-270%5Eo=27%5Eo ALIGN=MIDDLE  ALT=\"%2250+%27%22-270%5Eo=27%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2250+%27%22=approximately27.83333%5Eo ALIGN=MIDDLE  ALT=\"%2250+%27%22=approximately27.83333%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "while leg measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2250 ALIGN=MIDDLE  ALT=\"x%2B2250\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet is adjacent to the same angle.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2827.83333%5Eo%29=d%2F%28x%2B2250%29 ALIGN=MIDDLE  ALT=\"tan%2827.83333%5Eo%29=d%2F%28x%2B2250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BLC ALIGN=MIDDLE  ALT=\"BLC\"   DISABLED_style= \"max-width:90%; height:auto;\" > , a leg measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet is opposed to an angle measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=311%5Eo ALIGN=MIDDLE  ALT=\"311%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2255+%27%22-270%5Eo=41%5Eo ALIGN=MIDDLE  ALT=\"%2255+%27%22-270%5Eo=41%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2255+%27%22=approximately41.91667%5Eo ALIGN=MIDDLE  ALT=\"%2255+%27%22=approximately41.91667%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "while leg measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet is adjacent to the same angle.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2841.91667%5Eo%29=d%2Fx ALIGN=MIDDLE  ALT=\"tan%2841.91667%5Eo%29=d%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Dividing one equation vby the other, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29=%28x%2B2250%29%2Fx ALIGN=MIDDLE  ALT=\"tan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29=%28x%2B2250%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,which can be solved for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, we can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2841.91667%5Eo%29=d%2Fx ALIGN=MIDDLE  ALT=\"tan%2841.91667%5Eo%29=d%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=x%2Atan%2841.91667%5Eo%29 ALIGN=MIDDLE  ALT=\"d=x%2Atan%2841.91667%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29=%28x%2B2250%29%2Fx ALIGN=MIDDLE  ALT=\"tan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29=%28x%2B2250%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Atan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29=x%2B2250 ALIGN=MIDDLE  ALT=\"x%2Atan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29=x%2B2250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Atan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29-x=2250 ALIGN=MIDDLE  ALT=\"x%2Atan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29-x=2250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28tan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29-1%29=2250 ALIGN=MIDDLE  ALT=\"x%28tan%2841.91667%5Eo%29%2Ftan%2827.83333%5Eo%29-1%29=2250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29%2Ftan%2827.83333%5Eo%29=2250 ALIGN=MIDDLE  ALT=\"x%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29%2Ftan%2827.83333%5Eo%29=2250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29=2250%2Atan%2827.83333%5Eo%29 ALIGN=MIDDLE  ALT=\"x%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29=2250%2Atan%2827.83333%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2250%2Atan%2827.83333%5Eo%29%2F%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29 ALIGN=MIDDLE  ALT=\"x=2250%2Atan%2827.83333%5Eo%29%2F%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and finally<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=x%2Atan%2841.91667%5Eo%29=2250%2Atan%2827.83333%5Eo%29%2Atan%2841.91667%5Eo%29%2F%28tan%2841.91667%5Eo%29-tan%2827.83333%5Eo%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That calculates as approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=highlight%282884%29 ALIGN=MIDDLE  ALT=\"d=highlight%282884%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );