document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202999>Question 1202999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a town, Chief X resides 60m away on a bearing of 057° from the palace P, while Chief y resides on a bearing of 150° from the same palace P. The residence of X and Y are 180m apart.\r<BR>\n" );
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document.write( "(a) Illustrate the information in a diagram.\r<BR>\n" );
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document.write( "    Find, correct to three significant figures, the:\r<BR>\n" );
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document.write( "(i) bearing of X from Y;\r<BR>\n" );
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document.write( "(ii) distance between P and Y. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838214 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3821)</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=838214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "This is one way to draw the diagram.<BR>\n" );
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document.write( "The triangle XPY is shown above with extra helper points A,B,C.\r<BR>\n" );
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document.write( "Point A is directly north of P. <BR>\n" );
document.write( "Point A is useful to form the angles APX = 57 and APY = 150<BR>\n" );
document.write( "These are the bearing angles.<BR>\n" );
document.write( "The bearing angles have direct north as the starting direction, and then you turn clockwise toward the east when increasing the angles.\r<BR>\n" );
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document.write( "note:<BR>\n" );
document.write( "<font color=blue>(angle APX)</font> + <font color=purple>(angle XPY)</font> = <font color=red>angle APY</font><BR>\n" );
document.write( "<font color=blue>57°</font> + <font color=purple>93°</font> = <font color=red>150°</font>\r<BR>\n" );
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document.write( "Point B is north of Y to help set up angle BYX. See the next section below.\r<BR>\n" );
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document.write( "Point C is south of P so we can form angle CPY, which will help determine angle CYP.\r<BR>\n" );
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document.write( "For the next two parts, I'll give hints.\r<BR>\n" );
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document.write( "Part (i)\r<BR>\n" );
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document.write( "You'll need to...<ol><li>Determine angle BYX</li><li>Subtract that angle from 360 to find the reflex angle, so you can determine the bearing of X from Y.</li></ol>Note that<BR>\n" );
document.write( "(angle CYP) + (angle PYX) + (angle BYX) = 90\r<BR>\n" );
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document.write( "Angle CYP is complementary to angle CPY = 30 shown in the diagram.<BR>\n" );
document.write( "i.e.<BR>\n" );
document.write( "(angle CPY) + (angle CYP) = 90<BR>\n" );
document.write( "30 + (angle CYP) = 90<BR>\n" );
document.write( "I'll let you finish this part.\r<BR>\n" );
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document.write( "Angle PYX is determined through the law of sines<BR>\n" );
document.write( "Focus on triangle XPY to say:<BR>\n" );
document.write( "sin(P)/XY = sin(Y)/PX<BR>\n" );
document.write( "sin(93)/180 = sin(Y)/60<BR>\n" );
document.write( "I'll let you finish this part. <BR>\n" );
document.write( "This will determine angle PYX.\r<BR>\n" );
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document.write( "After determining angles CYP and PYX, you'll have enough info to determine angle BYX.\r<BR>\n" );
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document.write( "After finding angle BYX, subtract from 360.<BR>\n" );
document.write( "The goal is to compute: 360 - (angle BYX) <BR>\n" );
document.write( "so you can find the bearing of X from Y.\r<BR>\n" );
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document.write( "To answer part (ii), you can use either the law of sines or law of cosines to find the distance from P to Y.<BR>\n" );
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