document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200431>Question 1200431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boy cycles 8km on a bearing of 060°.<BR>\n" );
document.write( "How far is the boy North of his starting<BR>\n" );
document.write( "point? Give your answer to 2 s.f. </SPAN>\n" );
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document.write( "Start facing directly north.<BR>\n" );
document.write( "Then turn 60 degrees toward the east (i.e. to the right).<BR>\n" );
document.write( "This will align you with the bearing 060°<BR>\n" );
document.write( "This is in the northeast quadrant.\r<BR>\n" );
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document.write( "Compass Rose:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://upload.wikimedia.org/wikipedia/commons/e/e9/Compass_rose.png\"><BR>\n" );
document.write( "Image courtesy of Wikipedia.<BR>\n" );
document.write( "https://en.wikipedia.org/wiki/File:Compass_rose.png\r<BR>\n" );
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document.write( "This is what your rough sketch of the diagram should look like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-1%2C2%2C-1%2C-2%29%2C%0D%0Aline%28-1%2C-2%2C3%2C-2%29%2C%0D%0Aline%28-1%2C-2%2C2%2C1%29%2C%0D%0A%0D%0Alocate%28-1%2C-2%2C%22P%22%29%2C%0D%0Alocate%282%2C1%2C%22Q%22%29%2C%0D%0A%0D%0Alocate%28-0.8%2C-0.46%2C60%5Eo%29%2C%0D%0Alocate%280.14%2C-1.32%2C30%5Eo%29%2C%0D%0Alocate%280.66%2C0.2%2C%228%22%29%2C%0D%0Alocate%28-5%2C-4.5%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The boy starts at point P and moves to point Q.<BR>\n" );
document.write( "Note that 60+30 = 90.\r<BR>\n" );
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document.write( "Let's erase the vertical line and erase the \"60 degree\" label.<BR>\n" );
document.write( "I'll add in a vertical line from Q to drop down to the horizontal line.<BR>\n" );
document.write( "It has length x to represent how far north Q is compared to P.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-1%2C-2%2C2%2C-2%29%2C%0D%0Aline%28-1%2C-2%2C2%2C1%29%2C%0D%0Aline%282%2C1%2C2%2C-2%29%2C%0D%0A%0D%0Aline%281.7%2C-2%2C1.7%2C-1.7%29%2C%0D%0Aline%281.7%2C-1.7%2C2%2C-1.7%29%2C%0D%0A%0D%0Alocate%28-1%2C-2%2C%22P%22%29%2C%0D%0Alocate%282%2B0.1%2C1%2B0.3%2C%22Q%22%29%2C%0D%0Alocate%282%2C-2%2C%22R%22%29%2C%0D%0Alocate%282%2B0.2%2C-0.5%2C%22x%22%29%2C%0D%0A%0D%0Alocate%280.14-0.5%2C-1.32%2C30%5Eo%29%2C%0D%0Alocate%280.66-0.5%2C0.2-0.5%2C%228%22%29%2C%0D%0Alocate%28-5%2C-4.5%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The goal is to have a right triangle, so we can use a trig ratio to determine x.\r<BR>\n" );
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document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(30) = x/8<BR>\n" );
document.write( "x = 8*sin(30)<BR>\n" );
document.write( "x = 8*0.5<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "This value is exact. <BR>\n" );
document.write( "Make sure your calculator is in degree mode.\r<BR>\n" );
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document.write( "Answer: <font color=red>4 km</font><BR>\n" );
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