document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120134>Question 1120134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, \r<BR>\n" );
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document.write( "I am facing problem with this question-\r<BR>\n" );
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document.write( "During an expedition, the leader of a scout troop decided to save time by hiking around a wooded area between the base camp and a lake. The troop reached the lake by walking 30 minutes on a bearing of N60degree East, then 45 minutes on a bearing of N80degree West. (Our teacher gave this as 280 degree, and I think this is a typo error). The leader figured that they walked at an average speed of 3km/h. If they could have walked straight through the forested area at 1km/h, did the troop save any time by going around? If so, how much? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735811 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=735811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> well, there's a big difference between north 80 degrees west and north 280 degrees west.\r<BR>\n" );
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document.write( "north 280 degrees west would be the same as north 80 degrees east which doesn't make much sense, unless your instructor is deliberately trying to trick you.\r<BR>\n" );
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document.write( "assuming you are correct, then, once all is settled, you will wind up with  triangle ABC as shown in the diagram below.\r<BR>\n" );
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document.write( "side a is opposite angle A.<BR>\n" );
document.write( "side b is opposite angle B.<BR>\n" );
document.write( "side c is opposite angle C.\r<BR>\n" );
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document.write( "angle B is equal to 40 degrees.\r<BR>\n" );
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document.write( "length of side a = 45/60 * 3 = 2.25 kilometers.<BR>\n" );
document.write( "length of side c = 30/60 * 3 = 1.5 kilometers.<BR>\n" );
document.write( "length of side b is what you want to find.\r<BR>\n" );
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document.write( "since the speed is in kilometers per hour, we will translate the time to hours.\r<BR>\n" );
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document.write( "45 minutes is equal to 45/60 hours.<BR>\n" );
document.write( "30 minutes is equal to 30/60 hours.\r<BR>\n" );
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document.write( "you can find the length of side b by invoking the law of cosines.<BR>\n" );
document.write( "the triangle has been labeled the way it is to make translating to the law of cosines easier.\r<BR>\n" );
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document.write( "the formula to use is b = sqrt(a^2 + c^2 - 2 * a * c * cos(B))\r<BR>\n" );
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document.write( "this formula becomes b = sqrt(2.25^2 + 1.5^2 - 2 * 2.25 * 1.5 * cos(40)).\r<BR>\n" );
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document.write( "solve for b to get b = 1.46345481 kilometers.\r<BR>\n" );
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document.write( "since this distance is traveled at 1 kilometer per hour, and since 1 kilometer per hour is equal to 1/60 kilometers per minute, divide that by 1/60 to get the number of minutes.\r<BR>\n" );
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document.write( "you get 1.46345481 / (1/60) = 87.80728917.\r<BR>\n" );
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document.write( "if the troop went through the woods, it would have taken them 87.80728917 minutes.\r<BR>\n" );
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document.write( "it took them 75 minutes to go around the woods.\r<BR>\n" );
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document.write( "they saved 87.80728917 minus 75 = 12.80728917 minutes by going around.\r<BR>\n" );
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document.write( "the top diagram is the final triangle formed.\r<BR>\n" );
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document.write( "this is the final triangle that allowed us to use the law of cosines to find the length of side b.\r<BR>\n" );
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document.write( "the bottom diagram shows how angle B was determined to be equal to 40 degrees.\r<BR>\n" );
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document.write( "AB is 60 degrees north east.<BR>\n" );
document.write( "triangle ABD is formed by drawing vertical line from B to D.<BR>\n" );
document.write( "that makes triangle ABD a right triangle.<BR>\n" );
document.write( "angle A of this triangle is 30 degrees because it is complement to 60 degrees.<BR>\n" );
document.write( "angle D of this triangle is 90 degrees because it is the intersection of a vertical and horizontal line.<BR>\n" );
document.write( "angle B of this triangle is 60 degrees because sum of the angles of a triangle is 80 degrees.\r<BR>\n" );
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document.write( "angle B of triangle ABC is 40 degrees because 80 + 40 + 60 = 180 degrees.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/072003.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the other angles of triangle ABC can also be derived through either the use of the law of cosines or the law of sines.\r<BR>\n" );
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document.write( "i used an online law of cosines calculator at <a  rel=nofollow HREF= \"https://www.calculatorsoup.com/calculators/geometry-plane/triangle-law-of-cosines.php\" target = \"_blank\">https://www.calculatorsoup.com/calculators/geometry-plane/triangle-law-of-cosines.php</a>\r<BR>\n" );
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document.write( "it found the other two angles for me, saving me a lot of additional work that i didn't feel like doing.\r<BR>\n" );
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document.write( "the results are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/072004.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "in solving these types of problems, you will more then likely make use of the law of cosines or the law of sines.\r<BR>\n" );
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document.write( "in this problem, the law of cosines was used after find that angle B was 40 degrees \r<BR>\n" );
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document.write( " </SPAN>\n" );
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