document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109663>Question 1109663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Building A and B are 200m and 500m from Building C respectively. the buildings are connected by straight concrete roads so that the road between building A and B makes an angle of 25º30' with the road that connects buildings A and C. How far is building A from building B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724642 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=724642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> angles can be measured in degrees minutes seconds.\r<BR>\n" );
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document.write( "to convert to degrees:\r<BR>\n" );
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document.write( "you multiply the number of seconds by 3600 and add it to the degrees.\r<BR>\n" );
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document.write( "you multiply the number of minutes by 60 and add it to the degrees.\r<BR>\n" );
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document.write( "therefore 25 degrees 30 minutes is equal to 25 degrees + 30/60 = 25.5 degrees.\r<BR>\n" );
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document.write( "that's your angle formed by the road between A and B, and the road between A and C.\r<BR>\n" );
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document.write( "your triangle formed is triangle ABC.\r<BR>\n" );
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document.write( "side a is the side opposite angle A.\r<BR>\n" );
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document.write( "side b is the side opposite angle B.\r<BR>\n" );
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document.write( "side c is the side opposite angle C.\r<BR>\n" );
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document.write( "i believe you will first have to find angle B and then find angle C and then use the law of cosines to find the length of side c.\r<BR>\n" );
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document.write( "to find angle B, use the law of sines.\r<BR>\n" );
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document.write( "you will get a/sin(A) = b/sin(B).\r<BR>\n" );
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document.write( "this will become 500 / sin(25.5) = 200 / sin(B)\r<BR>\n" );
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document.write( "solve for sin(B) to get sin(B) = 200 * sin(25.5) / 500.\r<BR>\n" );
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document.write( "that will get you sin(B) = .1722044387.\r<BR>\n" );
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document.write( "then you use arcsin(.1722044387) to get angle (B) = 9.916014584 degrees.\r<BR>\n" );
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document.write( "since the sum of the angles of a triangle is always equal to 180 degrees, then subtract angle (A) and angle (B) from 180 to get angle (C) = 144.5839854 degrees.\r<BR>\n" );
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document.write( "now use the law of cosines to find the length of side c.\r<BR>\n" );
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document.write( "the law of cosines says c^2 = a^2 + b^2 - 2ab*cos(C).\r<BR>\n" );
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document.write( "since angle (C) = 144.5839854 degrees and side a = 500 and side b = 200, the formula becomes:\r<BR>\n" );
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document.write( "c^2 = 500^2 + 200^2 - 2*500*200*cos(144.5839854).\r<BR>\n" );
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document.write( "this results in c^2 = 452993.1701.\r<BR>\n" );
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document.write( "solve for c to get c = sqrt(452993.1701) = 673.047673 meters in length.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "here's my diagram:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/021601.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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