Law of sines  Trigonometric Ratios and Angle Measures
Law of sines
Lessons
Notes:
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 (sidesideangle)
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)!

2.
Given the following triangle $\triangle ABC$,