#1**0 **

\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}\)

Where A and B denotes the angle opposite to a and b respectively.

If you want to find A you have to have the length of sides a and b and the angle B.

So:

\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}\\ \dfrac{\sin A}{a}=\dfrac{\sin B}{b}\\ \sin A = \dfrac{a\sin B}{b}\\ A = \arcsin \left(\dfrac{a\sin B}{b}\right)\)

And,

\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}\\ b =\dfrac{a\sin B}{\sin A}\\ \dfrac{\sin B}{\sin A}=\dfrac{b}{a}\\ \sin B = \dfrac{b\sin A}{a}\\ B = \arcsin\left(\dfrac{b\sin A}{a}\right)\)

Just exchange all the 'A's into 'B's and all 'a's into 'b's you get the formula for B.

MaxWong
Feb 18, 2017