Find the area of a triangle with two sides of length $8$ cm and $6$ cm and an included angle of $30^\circ$.

Area $= \dfrac{1}{2}ab\sin C = \dfrac{1}{2}(8)(6)\sin 30^\circ = 24 \times \dfrac{1}{2} = 12$ cm$^2$. Using $\cos 30^\circ$ instead of $\sin 30^\circ$ gives $12\sqrt{3}$, and omitting the half gives 24.