document.write( "Question 1182677: A force of 100N acting horizontally to the right is to be combined with another force P acting upward to the right at an angle of 15 degrees with the vertical. If the resultant force of these two forces is 122.83N, solve force P.​\r
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\n" ); document.write( "\n" ); document.write( "-> Is it possible to use phytagorean theorem? I'm having a hard time understanding the problem. Please help.. \n" ); document.write( "
Algebra.Com's Answer #813718 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since it makes a 15o angle with the vertical, it makes a 75o angle with the\r\n" );
document.write( "horizontal.\r\n" );
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document.write( "Yes, you can use the Pythagorean theorem.  I made a mistake somewhere, but\r\n" );
document.write( "don't have time to find it and correct it. Maybe you can find the mistake.\r\n" );
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document.write( "      horizontal   |   vertical \r\n" );
document.write( "      components   |  components\r\n" );
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document.write( "   |P|cos(75o) N   ||P|sin(75o) N\r\n" );
document.write( "        100 N      |      0 N\r\n" );
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document.write( "|P|(cos(75o)+100 N |  |P|sin(75o) N\r\n" );
document.write( "               ______________________________________________________________ \r\n" );
document.write( "|Resultant| = √(sum of horizontal components)2 +(sum of vertical components)2\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "\"15079.85=%28abs%28P%29cos%2875%5Eo%29%2B100%29%5E2+%2B+%28abs%28P%29sin%2875%5Eo%29%29%5E2\"\r\n" );
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document.write( "\"15079.85=%28abs%28P%29cos%2875%5Eo%29%2B100%29%5E2+%2B+%28abs%28P%29sin%2875%5Eo%29%29%5E2\"\r\n" );
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document.write( "Subtract 10000 from both sides.\r\n" );
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document.write( "Since \"cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1\"\r\n" );
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document.write( "\"5079.84=abs%28P%29%5E2%281%29%2B200cos%2875%5Eo%29abs%28P%29\"\r\n" );
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document.write( "\"5079.84=abs%28P%29%5E2%2B200cos%2875%5Eo%29abs%28P%29\"\r\n" );
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document.write( "\"0=abs%28P%29%5E2%2B200cos%2875%5Eo%29abs%28P%29-5079.84\"\r\n" );
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document.write( "\"0=abs%28P%29%5E2%2B51.76380902abs%28P%29-5079.84\"\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
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document.write( "\"abs%28P%29+=+%28-51.76380902+%2B-+sqrt%282679.491924%2B20319.36%29%29%2F2+\"\r\n" );
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document.write( "\"abs%28P%29+=+%28-51.76380902+%2B-+sqrt%2822998.85192%29%29%2F2+\"\r\n" );
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document.write( "\"abs%28P%29+=+%28-51.76380902+%2B-+151.6537237%29%2F2+\"\r\n" );
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document.write( "We use the + since the - gives a negative value.\r\n" );
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document.write( "\"abs%28P%29+=+%28-51.76380902+%2B+151.6537237%29%2F2+\"\r\n" );
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document.write( "\"abs%28P%29+=+%28-51.76380902+%2B+151.6537237%29%2F2+\"\r\n" );
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document.write( "\"abs%28P%29+=+%2899.88991471%29%2F2+\"\r\n" );
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document.write( "\"abs%28P%29+=+49.94495735+\"\"N\"\r\n" );
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document.write( "That's the magnitude of the force P.\r\n" );
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document.write( "The angle it makes with the x-axis is found by\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"matrix%281%2C2%2Cvertical%2Ccomponents%29%2Fmatrix%281%2C2%2Chorizontal%2Ccomponents%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%28abs%28P%29sin%2875%5Eo%29%29%2F%28abs%28P%29cos%2875%5Eo%29%5E%22%22%2B100%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"%2849.94495735sin%2875%5Eo%29%29%2F%2849.94495735cos%2875%5Eo%29%5E%22%22%2B100%29\"\r\n" );
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document.write( "\"tan%28theta%29\"\"%22%22=%22%22\"\"0.0769820774\"\r\n" );
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document.write( "\"theta\"\"%22%22=%22%22\"\"4.402065933%5Eo\"\r\n" );
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document.write( "Edwin
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