document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186007>Question 1186007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the resultant of two forces acting at right angles to each other is 80 degrees N. If one of the forces is 45 deg N, what is the other force and the angle it makes with resultant </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849485 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=849485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem:\r<BR>\n" );
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document.write( "**1. Visualize the forces:**\r<BR>\n" );
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document.write( "Imagine the two forces (let's call them F1 and F2) acting at right angles.  Their resultant (R) is the vector sum of these forces.  We can visualize this as a right triangle, where F1 and F2 are the legs, and R is the hypotenuse.\r<BR>\n" );
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document.write( "**2. Use the Pythagorean theorem:**\r<BR>\n" );
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document.write( "R² = F1² + F2²\r<BR>\n" );
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document.write( "We know R = 80 N and F1 = 45 N.  We need to find F2.\r<BR>\n" );
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document.write( "80² = 45² + F2²<BR>\n" );
document.write( "6400 = 2025 + F2²<BR>\n" );
document.write( "F2² = 4375<BR>\n" );
document.write( "F2 = √4375 ≈ 66.14 N\r<BR>\n" );
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document.write( "**3. Find the angle between the resultant and the known force (F1):**\r<BR>\n" );
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document.write( "Let θ be the angle between the resultant (R) and F1. We can use trigonometry:\r<BR>\n" );
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document.write( "tan(θ) = F2 / F1<BR>\n" );
document.write( "tan(θ) = 66.14 / 45<BR>\n" );
document.write( "tan(θ) ≈ 1.47<BR>\n" );
document.write( "θ = arctan(1.47) ≈ 55.7°\r<BR>\n" );
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document.write( "**4. Find the angle between the resultant and the other force (F2):**\r<BR>\n" );
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document.write( "Since the forces are at right angles, the angle between F2 and the resultant will be 90° - θ.\r<BR>\n" );
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document.write( "Angle between R and F2 = 90° - 55.7° ≈ 34.3°\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "*   The other force (F2) is approximately **66.14 N**.<BR>\n" );
document.write( "*   The angle it makes with the resultant is approximately **34.3°**.<BR>\n" );
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