document.write( "Question 1076294: The sides of a triangle are 3 cm, 5 cm and 7 cm respectively. Show that the largest angle is 120 degree, and find the area of the triangle. \n" ); document.write( "

Algebra.Com's Answer #690950 by Fombitz(32388) $\"\"$ $\"About$

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Using the law of cosines,
\n" ); document.write( " $\"c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29\"$
\n" ); document.write( " $\"cos%28C%29=%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29%29\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"cos%28C%29=%283%5E2%2B5%5E2-7%5E2%29%2F%282%283%29%285%29%29\"$
\n" ); document.write( " $\"cos%28C%29=%289%2B25-49%29%2F30\"$
\n" ); document.write( " $\"cos%28C%29=%28-15%29%2F30\"$
\n" ); document.write( " $\"cos%28C%29=-1%2F2\"$
\n" ); document.write( " $\"C=120\"$
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\n" ); document.write( "To find the area, use Heron's formula,
\n" ); document.write( " $\"S=%283%2B5%2B7%29%2F2=15%2F2\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"A=sqrt%28S%28S-3%29%28S-5%29%28S-7%29%29\"$
\n" ); document.write( " $\"A=sqrt%28%2815%2F2%29%2815%2F2-6%2F2%29%2815%2F2-10%2F2%29%2815%2F2-14%2F2%29%29\"$
\n" ); document.write( " $\"A=sqrt%28675%2F16%29\"$
\n" ); document.write( " $\"A=%2815%2F4%29sqrt%283%29\"$ \n" ); document.write( "

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