document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207162>Question 1207162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the arch of this bridge is an arc of a circle. the arc measures 80 degrees and the bridge spans a 200 meters across a valley. what is the length of the bridge's arch? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844881 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Draw a circle centered at point A.<BR>\n" );
document.write( "Plot points B and C that are on the circle, and that are on the same horizontal level. <BR>\n" );
document.write( "Draw segment BC.<BR>\n" );
document.write( "Erase a big chunk of the circle so you're only left with minor arc BC.<BR>\n" );
document.write( "The arc has endpoints B and C.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Based on the values mentioned in the instructions, we can say that:<BR>\n" );
document.write( "Chord BC is 200 meters<BR>\n" );
document.write( "Angle BAC = 80 degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-4%2C6%2C%0D%0A%0D%0Acircle%280%2C0%2C0.05%29%2Ccircle%280%2C0%2C0.07%29%2Ccircle%280%2C0%2C0.09%29%2Ccircle%280%2C0%2C0.11%29%2Ccircle%280%2C0%2C0.13%29%2Ccircle%280%2C0%2C0.15%29%2Ccircle%28-2%2C2%2C0.05%29%2Ccircle%28-2%2C2%2C0.07%29%2Ccircle%28-2%2C2%2C0.09%29%2Ccircle%28-2%2C2%2C0.11%29%2Ccircle%28-2%2C2%2C0.13%29%2Ccircle%28-2%2C2%2C0.15%29%2Ccircle%282%2C2%2C0.05%29%2Ccircle%282%2C2%2C0.07%29%2Ccircle%282%2C2%2C0.09%29%2Ccircle%282%2C2%2C0.11%29%2Ccircle%282%2C2%2C0.13%29%2Ccircle%282%2C2%2C0.15%29%2C%0D%0A%0D%0Aline%28-2%2C2%2C2%2C2%29%2C%0D%0Aline%28-2%2C2%2C0%2C0%29%2Cline%280%2C0%2C2%2C2%29%2C%0D%0A%0D%0Aarc%280%2C0%2C2%2Asqrt%288%29%2C2%2Asqrt%288%29%2C225%2C315%29%2C%0D%0A%0D%0Alocate%280.1%2C-0.1%2C%22A%22%29%2Clocate%28-1.9-0.5%2C1.9%2C%22B%22%29%2Clocate%282.1%2C1.9%2C%22C%22%29%2C%0D%0A%0D%0Alocate%28-1.08%2B1%2C2.24%2B0.18%2C%22200%22%29%2Clocate%28-0.56%2B0.3%2C1.14%2B0.1%2C80%5Eo%29%2C%0D%0A%0D%0Alocate%28-4.8%2C-3%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let D be the midpoint of segment BC.<BR>\n" );
document.write( "This means BD = DC and BD is half of BC<BR>\n" );
document.write( "Therefore BD = 200/2 = 100 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Draw a segment AD to form triangles ABD and ACD.<BR>\n" );
document.write( "They are congruent right triangles. We can use the SSS (side side side) congruence theorem to prove this claim. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-4%2C6%2C%0D%0A%0D%0Acircle%280%2C0%2C0.05%29%2Ccircle%280%2C0%2C0.07%29%2Ccircle%280%2C0%2C0.09%29%2Ccircle%280%2C0%2C0.11%29%2Ccircle%280%2C0%2C0.13%29%2Ccircle%280%2C0%2C0.15%29%2Ccircle%28-2%2C2%2C0.05%29%2Ccircle%28-2%2C2%2C0.07%29%2Ccircle%28-2%2C2%2C0.09%29%2Ccircle%28-2%2C2%2C0.11%29%2Ccircle%28-2%2C2%2C0.13%29%2Ccircle%28-2%2C2%2C0.15%29%2Ccircle%282%2C2%2C0.05%29%2Ccircle%282%2C2%2C0.07%29%2Ccircle%282%2C2%2C0.09%29%2Ccircle%282%2C2%2C0.11%29%2Ccircle%282%2C2%2C0.13%29%2Ccircle%282%2C2%2C0.15%29%2Ccircle%280%2C2%2C0.05%29%2Ccircle%280%2C2%2C0.07%29%2Ccircle%280%2C2%2C0.09%29%2Ccircle%280%2C2%2C0.11%29%2Ccircle%280%2C2%2C0.13%29%2Ccircle%280%2C2%2C0.15%29%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C2%29%2Cline%28-2%2C2%2C2%2C2%29%2C%0D%0Aline%28-2%2C2%2C0%2C0%29%2Cline%280%2C0%2C2%2C2%29%2C%0D%0Aline%28-0.35%2C2%2C-0.35%2C1.65%29%2Cline%28-0.35%2C1.65%2C0%2C1.65%29%2C%0D%0A%0D%0Aarc%280%2C0%2C2%2Asqrt%288%29%2C2%2Asqrt%288%29%2C225%2C315%29%2C%0D%0A%0D%0Alocate%280.1%2C-0.1%2C%22A%22%29%2Clocate%28-1.9-0.5%2C1.9%2C%22B%22%29%2Clocate%282.1%2C1.9%2C%22C%22%29%2Clocate%280.1%2C1.9%2C%22D%22%29%2C%0D%0A%0D%0Alocate%28-1.08%2C2.24%2B0.18%2C%22100%22%29%2Clocate%28-0.56-0.1%2C1.14%2B0.1%2C40%5Eo%29%2C%0D%0A%0D%0Alocate%28-4.8%2C-3%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because we have congruent triangles, we know that <BR>\n" );
document.write( "angle DAB = angle DAC = 40<BR>\n" );
document.write( "These angles are half of angle BAC = 80.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's focus entirely on triangle ABD.<BR>\n" );
document.write( "We'll use a trig ratio to determine radius AB.<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(A) = BD/AB<BR>\n" );
document.write( "sin(40) = 100/AB<BR>\n" );
document.write( "AB = 100/sin(40)<BR>\n" );
document.write( "AB = 155.572382686 approximately is the radius<BR>\n" );
document.write( "Please make sure that your calculator is set to degrees mode.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's determine the circumference of this circle.<BR>\n" );
document.write( "C = 2pi*r<BR>\n" );
document.write( "C = 2pi*155.572382686<BR>\n" );
document.write( "C = 977.4901090956<BR>\n" );
document.write( "I used the calculator's stored version of pi to get the most accuracy possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is the approximate distance around the full circle.<BR>\n" );
document.write( "However, we don't want a full circle. <BR>\n" );
document.write( "Instead we just want the arc piece.<BR>\n" );
document.write( "80/360 = 2/9<BR>\n" );
document.write( "We want 2/9 of a full circle.<BR>\n" );
document.write( "(2/9)*977.4901090956 = 217.220024243467\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red>approximately 217.220024 meters</font><BR>\n" );
document.write( "This is the curved distance from B to C.<BR>\n" );
document.write( "Round this value however your teacher instructs.<BR>\n" );
document.write( "Your answer may vary depending how you rounded intermediate steps and what level of precision you use for pi.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );