document.write( "Question 282781: Two forces of 40lbs and 20lbs on an object. The angle is 40 degrees between them. What is the angle between the Resultant force and the larger force? \n" ); document.write( "
Algebra.Com's Answer #205293 by Edwin McCravy(20065)\"\" \"About 
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Two forces of 40lbs and 20lbs on an object. The angle is 40 degrees between them. What is the angle between the Resultant force and the larger force?
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document.write( "To draw the resulting force, complete a paralellogram\r\n" );
document.write( "by drawing a line through each arrowhead parallel to\r\n" );
document.write( "the other vector.  I'll draw them in green.  Notice\r\n" );
document.write( "the angle marked \"%22140%B0%22\" is so marked because it\r\n" );
document.write( "is supplementary to the \"%2240%B0%22\" angle, and \"%22180%B0%22-%2240%B0%22=%22140%B0%22\".:\r\n" );
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document.write( "Now I'll draw in the resultant R in red:\r\n" );
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document.write( "In the lower triangle we have a case of SAS, so we\r\n" );
document.write( "use the law of cosines first to find the magnitude\r\n" );
document.write( "of the resultant R (the red vector).\r\n" );
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document.write( "\"abs%28red%28R%29%29%5E2=40%5E2%2B20%5E2-2%2840%29%2820%29cos%28%22140%B0%22%29\"\r\n" );
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document.write( "\"abs%28red%28R%29%29%5E2=3225.671109\"\r\n" );
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document.write( "\"abs%28red%28R%29%29=56.79499194\"\r\n" );
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document.write( "Now we use the law of sines:\r\n" );
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document.write( "\"20%2Fsin%28theta%29=abs%28red%28R%29%29%2Fsin%28%22140%B0%22%29\"\r\n" );
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document.write( "\"abs%28red%28R%29%29sin%28theta%29=20sin%28%22140%B0%22%29\"\r\n" );
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document.write( "\"sin%28theta%29=20sin%28%22140%B0%22%29%2Fabs%28red%28R%29%29\"\r\n" );
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document.write( "\"sin%28theta%29=.226353623\"\r\n" );
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document.write( "\"theta=%2213.08248883%B0%22\"\r\n" );
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document.write( "Edwin
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