Question

A triangle has sides A, B, and C. The angle between sides A and B is `pi/3`. If side C has a length of `2` and the angle between sides B and C is `pi/12`, what is the length of side A?

Answer 1

In `\Delta ABC`, Let `\angle A=\frac{\pi}{12}, \angle C=\frac{\pi}{3}` & `AB=2` as per given data
Now, using sine rule in `\Delta ABC` as follows
`\frac{BC}{\sin\angle A }=\frac{AB}{\sin \angle C}`
`BC=\frac{AB\sin \angle A}{\sin \angleC}`
`=\frac{2\sin \frac{\pi}{12}}{\sin \frac{\pi}{3}}`
`=\frac{2\cdot \frac{\sqrt3-1}{2\sqrt2}}{ \frac{\sqrt3}{2}}`
`=\frac{\sqrt6-\sqrt2}{\sqrt3}`