document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199997>Question 1199997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During a rodeo, a clown runs 8.0 m north, turns 55° north of east, and runs<BR>\n" );
document.write( "3.5 m. Then, after waiting for the bull to come near, the clown turns due east<BR>\n" );
document.write( "and runs 5.0 m to exit the arena. What is the clown’s total displacement? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833990 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</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=833990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Hint:\r<BR>\n" );
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document.write( "This is one way to draw out the diagram<BR>\n" );
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document.write( "Segment BC may or may not be parallel to segment AD.\r<BR>\n" );
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document.write( "The rodeo clown follows the path from A, to B, to C, to D in that exact order.\r<BR>\n" );
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document.write( "A to B = go north 8.0 meters<BR>\n" );
document.write( "B to C = travel 3.5 meters at an angle 55 degrees north of east<BR>\n" );
document.write( "C to D = go east 5.0 meters<BR>\n" );
document.write( "This path ABCD is marked in black.\r<BR>\n" );
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document.write( "The blue segments form right triangle BEC, where the 90 degree angle is at point E.<BR>\n" );
document.write( "Let<BR>\n" );
document.write( "x = length of segment EC<BR>\n" );
document.write( "y = length of segment EB\r<BR>\n" );
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document.write( "You can use the trig ratios sine or cosine determine the approximate values of x and y.<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "cos(angle) = adjacent/hypotenuse\r<BR>\n" );
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document.write( "Example:<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(angle EBC) = x/3.5<BR>\n" );
document.write( "sin(angle EBC) = EC/BC<BR>\n" );
document.write( "sin(35) = x/3.5<BR>\n" );
document.write( "I'll let the student solve for x.<BR>\n" );
document.write( "Make sure your calculator is in degree mode.<BR>\n" );
document.write( "Determining the value of y involves a similar calculation.\r<BR>\n" );
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document.write( "After determining x and y, note how:<BR>\n" );
document.write( "segment AE = AB+EB = 8.0 + y<BR>\n" );
document.write( "segment ED = EC+CD = x + 5.0\r<BR>\n" );
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document.write( "Meaning we can determine the legs of right triangle AED.\r<BR>\n" );
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document.write( "The hypotenuse of triangle AED, shown in red, is the displacement vector. <BR>\n" );
document.write( "It's the straight line path that the clown would take if the clown went directly from start to finish. It's the shortest such path. <BR>\n" );
document.write( "This means the clown avoids any detours that waste time.\r<BR>\n" );
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document.write( "To find the length of the red vector, use the pythagorean theorem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a & b are the leg lengths in either order (sides AE and ED calculated earlier)<BR>\n" );
document.write( "c = hypotenuse = longest side = segment AD\r<BR>\n" );
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document.write( "I'll let the student do these calculations.<BR>\n" );
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