document.write( "Question 955642: A(2,-1), B(-3,4) and C(1,-5) form the vertices of a triangle. find the interior angles of the triangle \n" ); document.write( "
Algebra.Com's Answer #584957 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You could do it using the distances and the law of cosines, but\r\n" );
document.write( "it would be harder that way.  I'm sure your teacher wants you\r\n" );
document.write( "to do it the following way instead, where we find the angle\r\n" );
document.write( "between two lines:\r\n" );
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\n" ); document.write( "A(2,-1), B(-3,4) and C(1,-5) form the vertices of a triangle. find the interior angles of the triangle:
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document.write( "We use the slope formula to find the slopes of the sides of the\r\n" );
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document.write( "The slope of AB is -1\r\n" );
document.write( "The slope of BC is -2.25\r\n" );
document.write( "The slope of AC is 4\r\n" );
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document.write( "The angle q between two lines is given by\r\n" );
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document.write( "\"tan%28theta%29=%22%22+%2B-+%28%28m%5B1%5D-m%5B2%5D%29%2F%281%2Bm%5B1%5Dm%5B2%5D%29%29\"  \r\n" );
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document.write( "∠A is between AB and AC which we can see is obtuse\r\n" );
document.write( "(greater than 90°.\r\n" );
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document.write( "Substitute the slopes of AB and AC\r\n" );
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document.write( "Now find the reference angle from a calculator using \"%22%22%2B5%2F3\"\r\n" );
document.write( "and inverse tangent feature:\r\n" );
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document.write( "reference angle = 59.03624347°\r\n" );
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document.write( "But we can see that ∠A between the two lines AB and AC\r\n" );
document.write( "is obtuse, so its tangent is negative and ∠A is a second \r\n" );
document.write( "quadrant angle so we subtract from 180° and get \r\n" );
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document.write( "∠A = 120.9637565°\r\n" );
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document.write( "Substitute the slopes of AB and BC\r\n" );
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document.write( "∠B is between AB and BC which we can see is acute\r\n" );
document.write( "(less than 90°.\r\n" );
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document.write( "Substitute the slopes\r\n" );
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document.write( "Now find the reference angle from a calculator using +0.3846153846 \r\n" );
document.write( "and inverse tangent feature:\r\n" );
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document.write( "reference angle = 21.03751103°\r\n" );
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document.write( "We can see that ∠A between the two lines AB and BC\r\n" );
document.write( "is acute, so the tangent is positive so ∠B is the same\r\n" );
document.write( "as its reference angle, so \r\n" );
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document.write( "∠B = 21.03751103°\r\n" );
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document.write( "To find ∠C, you could do it the same way as the others, but\r\n" );
document.write( "the easy way is to add ∠A and ∠B and subtract from 180°.  So,\r\n" );
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document.write( "∠C = 37.99873244°\r\n" );
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document.write( "Edwin
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