document.write( "Question 83147: Two forces of 40 pounds and 20 pounds, respectively, act simultaneously on an object. The angle between the two forces is 40(degrees). Find the magnitude of the resultant, to the nearest tenth of a pound. Find the measure of the angle, between the resultant and the larger force. \n" ); document.write( "

Algebra.Com's Answer #60048 by Edwin McCravy(20060) $\"\"$ $\"About$

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Two forces of 40 pounds and 20 pounds, respectively, act simultaneously on an object. The angle between the two forces is 40(degrees). Find the magnitude of the resultant, to the nearest tenth of a pound. Find the measure of the angle, between the resultant and the larger force.\r
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document.write( "Complete the parallelogram by drawing a line parallel to each vector\r\n" );
document.write( "through the tip of the OTHER vector.\r\n" );
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document.write( "Since two adjacent angles of a parallelogram are supplementary, the\r\n" );
document.write( "angle at the lower right corner of the parallelogram is 180°-40² or 140°\r\n" );
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document.write( "Now we draw in the resultant vector R\r\n" );
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document.write( "Isolate the lower triangle. (You could isolate the top one\r\n" );
document.write( "just as well).  Label it triangle ABC\r\n" );
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document.write( "Solve for b (which is the magnitude of vector R, using the law \r\n" );
document.write( "of cosines:\r\n" );
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document.write( "b² = a² + c² - 2ac·cos(B)\r\n" );
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document.write( "b² = 20² + 40² - 2(20)(40)cos(140°)\r\n" );
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document.write( "b² = 400 + 1600 - 1600)(-.7660444431)\r\n" );
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document.write( "b² = 3225.671109\r\n" );
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document.write( "Use the principle of square roots:\r\n" );
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document.write( "b = 56.79499194\r\n" );
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document.write( "Since b is the magnitude of vector R, then\r\n" );
document.write( "the resultant force R to the nearest tenth\r\n" );
document.write( "of a pound is 56.8 lb.\r\n" );
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document.write( "Now we only need to find angle A for that\r\n" );
document.write( "is the angle between the larger force and\r\n" );
document.write( "the resultant.\r\n" );
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document.write( "The law of sines tells us that\r\n" );
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document.write( "cross-multiplying:\r\n" );
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document.write( "Use the inverse sine\r\n" );
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document.write( "       A = 13.08248883°\r\n" );
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document.write( "To the nearest degree, this is 13°\r\n" );
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document.write( "Edwin

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