Hello i am a bit confused when it comes to this law.
How do i know when the reciprocal form is to be used
And how do i know when its not to be used?
If anyone could make an example.
Thanks
Hello, Riazy!
It really doesn't matter which form you use.
. . $\displaystyle \frac{a}{\sin A} \,=\,\frac{b}{\sin B}\,=\,\frac{c}{\sin C}\,\text{ is equivalent to }\,\frac{\sin A}{a} \,=\,\frac{\sin B}{b} \,=\,\frac{\sin C}{c}$
However, depending on what you are seeking,
. . there is a more convenient choice.
Example: .$\displaystyle b = 7,\:A = 50^o,\:B = 60^o.\;\text{ Find }a.$
Since we want $\displaystyle a$, I would choose the form with $\displaystyle a$ on top.
. . $\displaystyle \frac{a}{\sin A} \,=\,\frac{b}{\sin B} \quad\Rightarrow\quad \frac{a}{\sin50^o} \,=\,\frac{7}{\sin60^o} \quad\Rightarrow\quad a \,=\,\frac{7\sin50^o}{\sin60^o}\;\text{ . . . etc.} $