**Law of Sine**

For any $\triangle$

*ABC*,

$\frac{a}{\sin(A)}$ $=\frac{b}{\sin(B)}$ $=\frac{c}{\sin(C)}$

and,

$\frac{\sin(A)}{a}$ $=\frac{\sin(B)}{b}$ $=\frac{\sin(C)}{c}$

Use the Law of Sine when given a

*pair*!

**Ambiguous case**

Ambiguous case of the Law of Sine arises when given SSA (side-side-angle)

Step 1) Use the

*given angle*to find the height of the triangle: $h=b \sin (A)$

Step 2) Check if,

$Side\;a$ < $h$, then

*no triangles*

$Side\;a=h$, then

*1 triangle*

$Side\;a$ > $h$, then

*1 triangle*

$h$ < $Side\;a$ < $Side\;b$, then

*2 triangles*

Step 3) Solve the triangle(s)!