There is a law that states that ...
"The side opposite to the largest angle is the largest side of the triangle"
you can check if the rule you have written is correct or not yourself.
Draw a line 2 cm long. Draw a right angled triangle with one angle 60 and other 30 degress in such a way that 60 degree angle lies on the 2cm line. Extend the line upwards at an angle of 90 degrees to the line drawn at 60 degrees.
the line will be more than 4 cm long. Take an example of a setsquare
 
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The angle and sides are propotional. That is , the side opposite the biggest angle will be the biggest. But, it is not always true that if an angle is double of other, then the respective side will also be double.
Take for an example of right angled isoceles triangle, having angle 90, 45 & 45. We know that the hypotenuse is equal to the half of the other sides, but we do know that the hypostenuse is the bigggest side.
 
Hence, the sides are propotional to the angle. So, we can say that the side opposite the bigger angle is bigger than the side opposite the half angle, though we cannot say the the side would be double of the other.
 
So, the answer is NO, there is no law like that and it is wrong.
 
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using sine's formula a/sina=b/sinb=c/sinc