Triangle diagram In the triangle ABC, AC = 3cm, BC = 2cm, $\angle$ BAC = $\theta$ and $\angle$ ABC = 2$\theta$. Calculate the value of $\theta$ correct to the nearest tenth of a degree.
The above is part of an A-Level exam question. I am assuming you use the sine rule to get $\theta$, but I am not sure how to extract this value. The answer is given as 41.4$^o$.
I have looked at the current proofs and rules given in textbook, but get stuck at:
$$\frac{\sin \theta}{2}=\frac{\sin 2\theta}{3}$$
Your attempt is fine. But then you need to know the formula $$\sin2\theta=2\sin\theta\cos\theta$$ After that it is easy. You get $\cos\theta=3/4$. Since $\theta,2\theta$ are angles in a triangle, there sum is less than $180^o$, so $\theta<60^o$ and you get $\theta=41.4^o$.