What is the nature of Triangle if AB/AC=1/2 angle (BAC)=60° What is the nature of  Triangle if $\frac{AB}{AC}=\frac12$ and $\angle BAC=60^{\circ}$?. Can we use ratio between side lengths?

Using common notation, $BC=a,CA=b,AB=c$
We have $\displaystyle\frac cb=\frac12\iff b=2c\  \ \ \ (1) $
Applying cosine rule $$\cos\angle BAC=\frac{b^2+c^2-a^2}{2bc}$$
Using $(1)$
$$\frac{(2c)^2+c^2-a^2}{2(2c)c}=\cos60^\circ=\frac12\implies a^2=\cdots$$
