document.write( "Question 975061: If the lengths of an isosceles triangle are 9.4 and 16, find the angles to the nearest degree.
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Algebra.Com's Answer #596874 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "There is no way to tell which of these triangles that is desired.\r\n" );
document.write( "So we do both.\r\n" );
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document.write( "Either way, the first thing to do is draw the altitude,(in green)\r\n" );
document.write( "which splits the base into two segments each half as long as the \r\n" );
document.write( "original base, 9.4/2 = 4.7 on the left and 16/2 = 8 on the right.\r\n" );
document.write( "The green altitude divides the isosceles triangles into two\r\n" );
document.write( "congruent right triangles, so that we can use trig ratios.  \r\n" );
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document.write( "In each we know the ADJACENT SIDE and the HYPOTENUSE, so we\r\n" );
document.write( "use COSINE.\r\n" );
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document.write( "In the figure on the left, we have\r\n" );
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document.write( "We use our calculator and find \r\n" );
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document.write( "Since all three angles of a triangle = 180°, we find the vertex angle:\r\n" );
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document.write( "180°-2(72.91740297°) = 34.16519407°\r\n" );
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document.write( "So the angles in the triangle on the left are:\r\n" );
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document.write( "Base angles = 72.91740297° each, vertex angle = 34.16519407°\r\n" );
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document.write( "Rounded to the nearest degree, 73°, 73°, 34°\r\n" );
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document.write( "In the figure on the right, we have\r\n" );
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document.write( "We use our calculator and find \r\n" );
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document.write( "Since all three angles of a triangle = 180°, we find the vertex angle:\r\n" );
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document.write( "180°-2(31.67243343°) = 116.6551331°\r\n" );
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document.write( "So the angles in the triangle on the right are:\r\n" );
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document.write( "Base angles = 31.67243343° each, vertex angle = 116.6551331°\r\n" );
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document.write( "Rounded to the nearest degree, 32°, 32°, 117°\r\n" );
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document.write( "[Notice that adding the rounded angles gives 181° not 180°, demonstrating\r\n" );
document.write( "that rounding always introduces error.  It's a matter of sacrificing\r\n" );
document.write( "accuracy for convenience.]\r\n" );
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document.write( "Edwin

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