document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109461>Question 1109461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an army navigation exercise, a group of soldiers hiked due south from base camp for 2.5 km to a water hole. From there, they turned 45° to the left, to head south-east for 1.6 km to a resting point. When the soldiers were at the resting point, how far (correct to one decimal place):<BR>\n" );
document.write( "a) east were they from the water hole?<BR>\n" );
document.write( "b) south were they from the water hole?<BR>\n" );
document.write( "c) were they in a straight line from base camp? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724455 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=724455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> point A is their base camp.\r<BR>\n" );
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document.write( "point B is the water hole which is 2.5 km directly south of point A.\r<BR>\n" );
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document.write( "point C is the rest point which is 1.6 km 45 degrees south east from point B.\r<BR>\n" );
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document.write( "point D is directly west from point C and directly south from point B.\r<BR>\n" );
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document.write( "points B, C, and D form right triangle BCD.\r<BR>\n" );
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document.write( "angles B and C in this triangle are each 45 degrees.\r<BR>\n" );
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document.write( "angle D is 90 degrees.\r<BR>\n" );
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document.write( "sin(B) = DC / BC.\r<BR>\n" );
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document.write( "this becomes sin(45) = DC / 1.6\r<BR>\n" );
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document.write( "solve for DC to get DC = 1.6 * sin(45) = 1.13137085 kilometers.\r<BR>\n" );
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document.write( "sin(C) = BD / BC.\r<BR>\n" );
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document.write( "this becomes sin(45) = BD / 1.6\r<BR>\n" );
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document.write( "solve for BD to get BD = 1.6 * sin(45) = 1.13137085 kilometers.\r<BR>\n" );
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document.write( "BD and DC are both 1.13137085 kilometers in length.\r<BR>\n" );
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document.write( "this makes right triangle BCD an isosceles right triangle.\r<BR>\n" );
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document.write( "the length of AD is the distance between the base camp and the point directly west of the rest point and directly south from the base camp.\r<BR>\n" );
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document.write( "this distance is 2.5 + 1.13137085 kilometers which is equal to 3.63137085 kilometers.\r<BR>\n" );
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document.write( "the points A, C, and D form right triangle ACD.\r<BR>\n" );
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document.write( "AD and DC are legs of this right triangle.\r<BR>\n" );
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document.write( "AC is the hypotenuse of this right triangle.\r<BR>\n" );
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document.write( "AC is also the straight line distance from point A to point C, which is the straight line distance from the base camp to the rest point.\r<BR>\n" );
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document.write( "by the pythogarus formula, [AD]^2 + [DC]^2 = [AC]^2\r<BR>\n" );
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document.write( "this makes [AC]^2 = to 3.63137085^2 + 1.13137085^2 = 14.46685425.\r<BR>\n" );
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document.write( "AC is equal to sqrt([AC]^2) which makes AC = 3.803531813 kilometers.\r<BR>\n" );
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document.write( "your questions are:\r<BR>\n" );
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document.write( "When the soldiers were at the rest point, how far (correct to one decimal place):<BR>\n" );
document.write( "a) east were they from the water hole?<BR>\n" );
document.write( "b) south were they from the water hole?<BR>\n" );
document.write( "c) were they in a straight line from base camp?\r<BR>\n" );
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document.write( "answer to a):\r<BR>\n" );
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document.write( "they were 1.13137085 kilometers east of the water hole.<BR>\n" );
document.write( "that would be the distance from point C to point D on the diagram.\r<BR>\n" );
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document.write( "answer to b):\r<BR>\n" );
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document.write( "they were 1.3137085 kilometers south of the water hole.<BR>\n" );
document.write( "that would be the distance from point D to point B on the diagram.\r<BR>\n" );
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document.write( "answer to c):\r<BR>\n" );
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document.write( "they were 3.803531813 kilometers away from the base camp in a straight line from the base camp to the rest point.<BR>\n" );
document.write( "that would be the distance form point A to point C on the diagram.\r<BR>\n" );
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document.write( "you should round your answer to the number of decimal places required.\r<BR>\n" );
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document.write( "here's the diagram:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/021402.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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