The ratio of the sides of triangle ABC is 1:s | vedclass

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(D) Given the ratio of sides $a:b:c = 1:\sqrt{3}:2$.Let $a = \lambda$,$b = \sqrt{3}\lambda$,and $c = 2\lambda$.Using the Law of Cosines,$\cos A = \fra

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$1:2:3$

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(D) Given the ratio of sides $a:b:c = 1:\sqrt{3}:2$.Let $a = \lambda$,$b = \sqrt{3}\lambda$,and $c = 2\lambda$.Using the Law of Cosines,$\cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{3\lambda^2 + 4\lambda^2 - \lambda^2}{2(\sqrt{3}\lambda)(2\lambda)} = \frac{6\lambda^2}{4\sqrt{3}\lambda^2} = \frac{\sqrt{3}}{2}$.Thus,$A = 30^\circ$.Similarly,$\cos B = \frac{a^2 + c^2 - b^2}{2ac} = \frac{\lambda^2 + 4\lambda^2 - 3\lambda^2}{2(\lambda)(2\lambda)} = \frac{2\lambda^2}{4\lambda^2} = \frac{1}{2}$.Thus,$B = 60^\circ$.Finally,$C = 180^\circ - (30^\circ + 60^\circ) = 90^\circ$.The ratio $A:B:C = 30^\circ:60^\circ:90^\circ = 1:2:3$.

The ratio of the sides of triangle $ABC$ is $1:\sqrt{3}:2$. The ratio of angles $A:B:C$ is

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