1. The problem involves understanding and applying the Double Sine Law, which is used in solving triangles when two angles and one side or two sides and a non-included angle are known. 2. The Double Sine Law states that for any triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$ respectively, the ratio of the length of a side to the sine of its opposite angle is constant: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 3. This law helps find unknown sides or angles in a triangle when certain measurements are given. 4. To use the Double Sine Law, identify the known sides and angles, then set up the proportion accordingly. 5. For example, if you know $a$, $A$, and $B$, you can find $b$ by: $$b = \frac{a \sin B}{\sin A}$$ 6. Always ensure angles are in the same unit (degrees or radians) when calculating sines. 7. This law is especially useful in non-right triangles where the Pythagorean theorem does not apply. 8. Remember that the sine function is positive in the first and second quadrants, so check for ambiguous cases when solving for angles. This explanation covers the Double Sine Law and how to apply it to solve triangles.