document.write( "Question 387508: find, correct to the nearest degree the three angles of a triange with vertices A(0,3,3) B(-2,1,1) C(1,5,-1) \n" ); document.write( "

Algebra.Com's Answer #273964 by Edwin McCravy(20081) $\"\"$ $\"About$

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find, correct to the nearest degree the three angles of a triange with vertices A(0,3,3) B(-2,1,1) C(1,5,-1)
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document.write( "The line segment AB is parallel to the vector < -2-0,1-3,1-3 > = < -2,-2,-2 >\r\n" );
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document.write( "The line segment AC is parallel to the vector < 1-0,5-3,-1-3 > = <  1, 2,-4 >\r\n" );
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document.write( "The line segment BC is parallel to the vector < 1-(-2),5-1,-1-1 > = <  3, 4,-2 >\r\n" );
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document.write( "We use this formula\r\n" );
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document.write( "Angle A is the angle between AB and AC, which is the same angle\r\n" );
document.write( "as the angle between the vectors < -2,-2,-2 > and <  1, 2,-4 >\r\n" );
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document.write( "Their dot product is \r\n" );
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document.write( "< -2,-2,-2 >@<  1, 2,-4 > = (-2)(1)+(-2)(2)+(-2)(-4) = -2-4+8 = 2\r\n" );
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document.write( "The norm of < -2,-2,-2 > is  \r\n" );
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document.write( "The norm of < 1,2,-4 > is \r\n" );
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document.write( "Substituting in the formula for the cosine,\r\n" );
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document.write( "=.1259881577\r\n" );
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document.write( "So A = 82.76217579° or 83° to the nearest degree.\r\n" );
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document.write( "Find the other two angles the same way.\r\n" );
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document.write( "Edwin

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