document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139458>Question 1139458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this trigonometry word problem? here goes:\r<BR>\n" );
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document.write( "A helicopter maintains an elevation of 3.5 miles and<BR>\n" );
document.write( "is flying toward a control tower. The angle of elevation from the<BR>\n" );
document.write( "tower to the helicopter is x radians.\r<BR>\n" );
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document.write( "Figure: https://i.imgur.com/ncirDGi.png\r<BR>\n" );
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document.write( "1. The distance d must be written in miles, between the tower and the heli-copter as a function of x.\r<BR>\n" );
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document.write( "2. In this step, d must be found when x = 1 and x = 1.2. Then you must round to the nearest hundredth of a mile.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #759932 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=759932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's your diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/ncirDGi.png\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "label the left bottom corner of the triangle A, the top right corner of the triangle B and the bottom right corner of the triangle C.\r<BR>\n" );
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document.write( "angle x is at the A corner of the triangle, which is also called angle BAC.\r<BR>\n" );
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document.write( "the hypotenuse of the triangle is line segment AB, which we'll call d, because that's the distance from the helicopter to the top of the tower.\r<BR>\n" );
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document.write( "the sine of angle x is equal to opposite / hypotenuse which is equal to 3.5 / d.\r<BR>\n" );
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document.write( "you get sin(x) = 3.5 / d\r<BR>\n" );
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document.write( "solve for d to get d = 3.5 / sin(x)\r<BR>\n" );
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document.write( "x apprears to be in radians, so we'll go with that.\r<BR>\n" );
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document.write( "when x = 1, you get d = 3.5 / sin(1) = 3.5 / .8414709848 = 4.15938287 miles from the control tower.\r<BR>\n" );
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document.write( "when x = 1.2, you get d = 3.5 / sin(1.2) = 3.5 / .932039086 = 3.755207322 miles from the control tower.\r<BR>\n" );
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document.write( "the helicopter will be 3.5 miles from the control tower when angle x is equal to pi/2.\r<BR>\n" );
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document.write( "you get d = 3.5 / sin(pi/2) = 3.5\r<BR>\n" );
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document.write( "that's because the helicopter will be directly above the control tower when x = pi/2.\r<BR>\n" );
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document.write( "to convert the angles to degrees, you would multiply the radians by 180 / pi.\r<BR>\n" );
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document.write( "1 radian * 180 / pi is equal to 57.29577951 degrees.\r<BR>\n" );
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document.write( "1.2 radians * 180 / pi is equal to 68.75493542 degrees.\r<BR>\n" );
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document.write( "pi/2 radians * 180 / pi = 90 degrees.\r<BR>\n" );
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document.write( "your solutuion, rounded to the nearest hundredth of a mile, will be:\r<BR>\n" );
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document.write( "when x = 1, d = 4.16 miles.\r<BR>\n" );
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document.write( "when x = 1.2, d = 3.76 miles. </SPAN>\n" );
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