Working Backwards

If the area is known, the same rule finds a missing side. Write the rule with the area in place and solve for the side.

A triangle of area 24 has sides 8 and s with 30° between them: $24 = \frac{1}{2}\cdot 8\cdot s\cdot \sin\left(30^{\circ}\right)$, which is 24 = 2s, so s = 12. With an angle off the tables the board keeps the sine exact, divides by it, and you round at the end.