document.write( "Question 963851: The congruent angles of an isosceles triangle are 1/3of the vertex angle. Find the area of the congruent sides are 14in \n" ); document.write( "

Algebra.Com's Answer #588835 by josgarithmetic(39630) $\"\"$ $\"About$

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x, degree measure of vertex angle;
\n" ); document.write( " $\"2%28x%2F3%29%2Bx=180\"$
\n" ); document.write( " $\"2x%2B3x=3%2A180\"$
\n" ); document.write( " $\"5x=3%2A180\"$
\n" ); document.write( " $\"x=3%2A2%2A5%2A18%2F5\"$
\n" ); document.write( " $\"x=6%2A18\"$
\n" ); document.write( " $\"x=108\"$ \r
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\n" ); document.write( "\n" ); document.write( "The base angles each are $\"108%2F3=36\"$ degree.\r
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\n" ); document.write( "\n" ); document.write( "Altitude from vertex to the base cuts the isosceles triangle into TWO congruent right triangles with hypotenuse 14 inches, from the given descriptive question. This altitude segment is opposite the 36 degree angle. At the vertex location is a 54 degree angle. DRAW that much of this to show the angles and segments.\r
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\n" ); document.write( "\n" ); document.write( "Now you want to know the size of the altitude.
\n" ); document.write( "Altitude is $\"14%2Acos%2854%29\"$ ;
\n" ); document.write( "The half of the isosceles base would be $\"14%2Acos%2836%29\"$ .
\n" ); document.write( "That means the entire base of the isosceles triangle is $\"28%2Acos%2836%29\"$ .
\n" ); document.write( "Using area formula for a triangle, the area would be $\"%281%2F2%29%28base%29%28altitude%29\"$ , which you can fill-in and compute. \n" ); document.write( "

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