document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178041>Question 1178041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The resultant force of F1(150N, 030) and F2( x N, 120) is R(y N, 090). Find, correct to two decimal places, the values of x 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 #850374 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850374\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Resolve Forces into Components**\r<BR>\n" );
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document.write( "* **F1 (150N, 030°):**<BR>\n" );
document.write( "    * F1x = 150 * cos(30°) = 150 * (√3 / 2) ≈ 129.90 N<BR>\n" );
document.write( "    * F1y = 150 * sin(30°) = 150 * (1/2) = 75 N\r<BR>\n" );
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document.write( "* **F2 (x N, 120°):**<BR>\n" );
document.write( "    * F2x = x * cos(120°) = x * (-1/2) = -x/2 N<BR>\n" );
document.write( "    * F2y = x * sin(120°) = x * (√3 / 2) ≈ 0.866x N\r<BR>\n" );
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document.write( "* **R (y N, 090°):**<BR>\n" );
document.write( "    * Rx = y * cos(90°) = y * 0 = 0 N<BR>\n" );
document.write( "    * Ry = y * sin(90°) = y * 1 = y N\r<BR>\n" );
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document.write( "**2. Set Up Equations for Resultant Force**\r<BR>\n" );
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document.write( "The resultant force is the vector sum of the individual forces:\r<BR>\n" );
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document.write( "* Rx = F1x + F2x<BR>\n" );
document.write( "* Ry = F1y + F2y\r<BR>\n" );
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document.write( "Substitute the component values:\r<BR>\n" );
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document.write( "* 0 = 129.90 - x/2<BR>\n" );
document.write( "* y = 75 + 0.866x\r<BR>\n" );
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document.write( "**3. Solve for x**\r<BR>\n" );
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document.write( "From the first equation:\r<BR>\n" );
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document.write( "* x/2 = 129.90<BR>\n" );
document.write( "* x = 129.90 * 2<BR>\n" );
document.write( "* x = 259.80 N\r<BR>\n" );
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document.write( "**4. Solve for y**\r<BR>\n" );
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document.write( "Substitute the value of x into the second equation:\r<BR>\n" );
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document.write( "* y = 75 + 0.866 * 259.80<BR>\n" );
document.write( "* y = 75 + 224.9928<BR>\n" );
document.write( "* y = 299.9928 N\r<BR>\n" );
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document.write( "**5. Round to Two Decimal Places**\r<BR>\n" );
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document.write( "* x ≈ 259.80 N<BR>\n" );
document.write( "* y ≈ 299.99 N\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* x ≈ 259.80 N<BR>\n" );
document.write( "* y ≈ 299.99 N<BR>\n" );
document.write( " </SPAN>\n" );
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