document.write( "Question 302580: What are the angle measures of an isosceles triangle whose base is half as long as its congruent legs? (Round to the nearest tenth.) \n" ); document.write( "

Algebra.Com's Answer #216961 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "To avoid too many fractions, let's choose the congruent sides to have\r\n" );
document.write( "measure 4 each and the base half that or 2, then we'll be able to \r\n" );
document.write( "take half the base without having a fraction for the measure of a side: \r\n" );
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document.write( "Draw a median from the vertex angle which is also the perpendicular\r\n" );
document.write( "bisector as well as the bisector of the vertex angle.  That divides\r\n" );
document.write( "the triangle into two congruent right triangles, each with a base\r\n" );
document.write( "of measure 1:\r\n" );
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document.write( "We see that the cosine of the indicated angle is the adjacent\r\n" );
document.write( "side over the hypotenuse, that is\r\n" );
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document.write( "Use a calculator to find the inverse cosine of  or \r\n" );
document.write( "and you get\r\n" );
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document.write( "So each base angle has measure 75.5° (rounded to tenths). So\r\n" );
document.write( "doubling that to account for the measures of the two base angles\r\n" );
document.write( "we get 151°, then subtracting that from 180° gives the vertex angle\r\n" );
document.write( "having measure 29°.\r\n" );
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document.write( "Edwin

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