document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=497455>Question 497455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.the area of the triangle with sides 36 meters, 54 meters, 77 meters?<BR>\n" );
document.write( "2.two m16 rifles are stock to the ground. the first rifle is 99 cm in length while the other is attached to a bayonet knife having length of 112 cm if the angle formed by two rifles is 50 degrees, determine the distance between the butt plates of the rifles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #336737 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=336737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can use heron's formula to find the area of the triangle when given 3 sides.\r<BR>\n" );
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document.write( "heron's formula is:<BR>\n" );
document.write( "a = sqrt(s(s-a)(s-b)(s-c)) where:<BR>\n" );
document.write( "a = area<BR>\n" );
document.write( "s = (a + b + c)/2<BR>\n" );
document.write( "s can also be shown as p/2 where:<BR>\n" );
document.write( "p = a + b + c\r<BR>\n" );
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document.write( "in your triangle:<BR>\n" );
document.write( "a = 36<BR>\n" );
document.write( "b = 54<BR>\n" );
document.write( "c = 77\r<BR>\n" );
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document.write( "using heron's formula, we get:<BR>\n" );
document.write( "p = a + b + c = 167<BR>\n" );
document.write( "p/2 = 167/2 = 83.5<BR>\n" );
document.write( "a = sqrt(s(s-a)*(s-b)*s-c)) becomes:<BR>\n" );
document.write( "a = sqrt(83.5(47.5)(29.5)(6.5)) which becomes:<BR>\n" );
document.write( "a = 872.0828157\r<BR>\n" );
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document.write( "here's a solver from one of the folks at algebra.com that give you the answer with a lot less effort on your part.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Triangles/Find-the-area-of-triangle-if-3-sides-are-given.solver\" target= \"_blank\">http://www.algebra.com/algebra/homework/Triangles/Find-the-area-of-triangle-if-3-sides-are-given.solver</a>\r<BR>\n" );
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document.write( "it's good to know the formula though.<BR>\n" );
document.write( "on a test, you won't have access to the nifty little tool developed here.<BR>\n" );
document.write( "best thing is to do the calculations yourself and then use the tool to check your work.\r<BR>\n" );
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document.write( "you could also have solved for the area using the law of cosines but it's a lot more work.<BR>\n" );
document.write( "kudos to heron.\r<BR>\n" );
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document.write( "your second problem is different because you are given an angle.<BR>\n" );
document.write( "assume your triangle is labeled ABC.<BR>\n" );
document.write( "The angle that is 50 degrees would be A.<BR>\n" );
document.write( "The side that is 99 cm in length would be AB.<BR>\n" );
document.write( "The side that is 112 cm in length would be AC.<BR>\n" );
document.write( "BC is the side opposite angle A, the length of which is unknown.\r<BR>\n" );
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document.write( "you want to find the length of BC which is the distance between the butts of each rifle.\r<BR>\n" );
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document.write( "you can use the law of cosines here.<BR>\n" );
document.write( "re-label your triangle as follows:<BR>\n" );
document.write( "AB = c<BR>\n" );
document.write( "AC = b<BR>\n" );
document.write( "BC = a<BR>\n" );
document.write( "AB is opposite angle C which means that c is opposite angle C<BR>\n" );
document.write( "AC is opposite angle B which means that b is opposite angle B<BR>\n" );
document.write( "BC is opposite angle A which means that a is opposite angle A\r<BR>\n" );
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document.write( "the law of cosines states:\r<BR>\n" );
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document.write( "a^2 = b^2 + c^2 - 2*b*c*cos(A)\r<BR>\n" );
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document.write( "substitute known values into this formula to get:\r<BR>\n" );
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document.write( "a^2 = 112^2 + 99^2 - 2*112*99*cos(50) which becomes:<BR>\n" );
document.write( "a^2 = 12544 + 9801 - 22176*.64278761 which becomes:<BR>\n" );
document.write( "a^2 = 8090.541968<BR>\n" );
document.write( "take square root of both sides of this equation to get:<BR>\n" );
document.write( "a = 89.94744003\r<BR>\n" );
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document.write( "your triangles look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2011/sep141.jpg\" alt = \"$$$$$\" />\r<BR>\n" );
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document.write( " </SPAN>\n" );
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