Problem is, given Fig1, If AB = 34, solve for CB.
My main difficulty with this problem is that I don't know how to correctly set a proportion with triangle ADB and triangle ADC.
If so, I could make a proportion between the sides of the triangles such that X/Y = CB/34
where X and Y are just numbers, then I could easily solve for CB.
Maybe use Thales' theorem? If so, how? Any help is welcome.
Using law of sines in $\triangle ABC$, we have
$$\frac{AB}{\sin 127^{\circ}} = \frac{CB}{\sin16^{\circ}}$$
Hence,
$$CB = \frac{34 \sin16^{\circ}}{\sin127^{\circ}}$$