document.write( "Question 725621: Find the interior angles of the triangle with the given vertices (1,2) (3,4) (2,5) \n" ); document.write( "

Algebra.Com's Answer #444257 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find the interior angles of the triangle with the given vertices (1,2) (3,4) (2,5)
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document.write( "You can do this two different ways.\r\n" );
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document.write( "Method 1:\r\n" );
document.write( "A. Use the distance formula to find the length of the three sides.\r\n" );
document.write( "B. Use then law of cosines.\r\n" );
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document.write( "Method 2:\r\n" );
document.write( "1. Find the slopes of the three sides.\r\n" );
document.write( "2. Use the tangent formula for the angles between two sides.\r\n" );
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document.write( "Method 2 is easier.\r\n" );
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document.write( "Let's draw the triangle and extend the sides:\r\n" );
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document.write( "(1,2) (3,4) (2,5)\r\n" );
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document.write( "We  use the slope formula, which is\r\n" );
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document.write( "m = \r\n" );
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document.write( "three times to find these three slopes:\r\n" );
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document.write( "the slope of the green line is m = 1\r\n" );
document.write( "the slope of the red line is m = 3\r\n" );
document.write( "the slope of the blue line is m = -1\r\n" );
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document.write( "Here is the formula for the acute angle between two lines, one with\r\n" );
document.write( "slope m₁  and the other with slope m₂.\r\n" );
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document.write( "with each pair of lines.  Except when two lines are perpendicular\r\n" );
document.write( "there are TWO angles between any pair of lines, an acute angle and an\r\n" );
document.write( "obtuse angle which are supplementary.      \r\n" );
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document.write( "If the denominator of that fraction\r\n" );
document.write( "comes out 0, making it undefined, that means the angle between\r\n" );
document.write( "the two lines are perpendicular and the angle between them is 90°.\r\n" );
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document.write( "I'll just find the angle between the green and red lines. You find\r\n" );
document.write( "the others:\r\n" );
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document.write( "Using the inverse tangent function on a calculator, we get\r\n" );
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document.write( "q = 26.56505118°.\r\n" );
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document.write( "That's the acute angle between the green and red lines.\r\n" );
document.write( "The obtuse angle between them is 180°-26.56505118° or 153.4349488°\r\n" );
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document.write( "The acute angle between the red and blue lines is 63.43494882°\r\n" );
document.write( "The obtuse angle between them is 180°-63.43494882° or 116.5650512°.\r\n" );
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document.write( "The angle between the green and blue line is 90°.  (You can also\r\n" );
document.write( "tell that because their slopes are negative reciprocals 1 and -1.)\r\n" );
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document.write( "Since it is a right triangle the other two angles besides the\r\n" );
document.write( "right angle are acute angles.\r\n" );
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document.write( "Answers: 26.56505118°, 63.43494882°, 90° \r\n" );
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document.write( "Edwin

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