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Question Number 113807 by deepraj123 last updated on 15/Sep/20

$$\mathrm{In}\mathrm{any}△ABC,\mathrm{if}\mathrm{the}\mathrm{angles}\mathrm{are}\mathrm{in}$$$$\mathrm{the}\mathrm{ratio}1:2:3,\mathrm{then}\mathrm{the}\mathrm{ratio}\mathrm{of}$$$$\mathrm{corresponding}\mathrm{sides}\mathrm{is}$$

Answered by bemath last updated on 15/Sep/20

$$\mathrm{\angle }A=k,\mathrm{\angle }B=2k,\mathrm{\angle }C=3k$$$$\Rightarrow 6k=180°\to k=30°$$$$\frac{a}{\sin 30°}=\frac{b}{\sin 60°}=\frac{c}{\sin 90°}$$$$\frac{a}{\frac{1}{2}}=\frac{b}{\frac{1}{2}\sqrt{3}}=\frac{c}{1}\to \{\begin{array}{l}b=\frac{1}{2}\sqrt{3}c\\ a=\frac{1}{2}c\end{array}$$$$a:b:c=\frac{1}{2}:\frac{1}{2}\sqrt{3}:1$$$$=1:\sqrt{3}:2$$$$$$

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