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Question Number 49984 by behi83417@gmail.com last updated on 12/Dec/18

Commented by behi83417@gmail.com last updated on 12/Dec/18

$$A\stackrel{△}{BC},equilateral.AB=a,A\stackrel{}{CE}=\alpha .$$$$find:AD,BD,intermsofaand\alpha .$$

Answered by mr W last updated on 12/Dec/18

$$R=\frac{\sqrt{3}a}{3}$$$$AD=2R\sin \alpha =\frac{2\sqrt{3}a\sin \alpha }{3}$$$$BD=2R\sin (\frac{\pi }{3}-\alpha )=\frac{2\sqrt{3}a}{3}(\frac{\sqrt{3}}{2}\cos \alpha -\frac{1}{2}\sin \alpha )$$$$BD=\frac{(3\cos \alpha -\sqrt{3}\sin \alpha )a}{3}$$

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