In a triangle ABC,if r_1 = 2r_2 = 3r_3,then s | vedclass

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(D) Given,in $	riangle ABC$,$r_1 = 2r_2 = 3r_3$. We know that $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$. L

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$5 : 4 : 3$

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(D) Given,in $	riangle ABC$,$r_1 = 2r_2 = 3r_3$. We know that $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$. Let $\frac{\Delta}{s-a} = \frac{2\Delta}{s-b} = \frac{3\Delta}{s-c} = \frac{1}{K}$. Then $s-a = K$,$s-b = 2K$,and $s-c = 3K$. Adding these,$(s-a) + (s-b) + (s-c) = K + 2K + 3K = 6K$. $3s - (a+b+c) = 6K$ $\Rightarrow 3s - 2s = 6K$ $\Rightarrow s = 6K$. Thus,$a = s - K = 5K$,$b = s - 2K = 4K$,and $c = s - 3K = 3K$. Using the sine rule,$\sin A : \sin B : \sin C = a : b : c = 5K : 4K : 3K = 5 : 4 : 3$.

In a triangle $ABC$,if $r_1 = 2r_2 = 3r_3$,then $\sin A : \sin B : \sin C =$

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