document.write( "Question 1101717: The ratio of the side of traingle is 2:√6:1+√3.
\n" ); document.write( "Find the ratio of the measure of the angles \n" ); document.write( "
Algebra.Com's Answer #716328 by Boreal(15235)\"\" \"About 
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Draw this and let angle a be opposite to 2, angle b opposite to side sqrt(6) and angle c be opposite to side (1+ sqrt(3)).
\n" ); document.write( "Law of cosines
\n" ); document.write( "a^2=b^2+c^2-2bc cos A
\n" ); document.write( "4=6+(2.732)^2-2(sqrt (6)*(1+sqrt(3)) cos A
\n" ); document.write( "numerically
\n" ); document.write( "4=6+7.46-2*6.69 cos A
\n" ); document.write( "-9.46=-13.38 cos A
\n" ); document.write( "cos A=9.46/13.38
\n" ); document.write( "arc cos both
\n" ); document.write( "A=45.0 degrees.
\n" ); document.write( "find b
\n" ); document.write( "b^2=a^2+c^2-2ac cos B
\n" ); document.write( "6=4+7.46-2(2*2.732) cos B
\n" ); document.write( "-5.46=-10.93 cos B
\n" ); document.write( "cos B=0.4995
\n" ); document.write( "B=60.0 degrees.
\n" ); document.write( "find c (besides subtracting 45 and 60 from 180)
\n" ); document.write( "c^2=a^2+b^2-2ab cos C
\n" ); document.write( "7.46=4+6-2(2 sqrt(6)) cos C
\n" ); document.write( "-2.54=-4 sqrt(6) cos C
\n" ); document.write( "-2.54=-9.80 cos C
\n" ); document.write( "cos C=2.54/9.80=75.0 deg (rounding from 74.97)
\n" ); document.write( "The ratios are 45:60:75 or 3:4:5
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