Problem: In triangle ABC, the angles satisfy $A=70^\circ$, $B=50^\circ$, and the side length $c=18$. Find the side $a$ to two decimal places. 1. The sum of the angles in a triangle is 180 degrees. Compute angle $C$ as follows. $$C=180^\circ-70^\circ-50^\circ=60^\circ$$ 2. Use the Law of Sines which states that the sides are proportional to the sines of the opposite angles. $$\frac{a}{\sin A}=\frac{c}{\sin C}$$ Solve for $a$ and substitute the known values. $$a=c\cdot\frac{\sin A}{\sin C}$$ $$a=18\cdot\frac{\sin 70^\circ}{\sin 60^\circ}$$ 3. Evaluate the trigonometric values and compute numerically. $$\sin 70^\circ\approx 0.9396926208$$ $$\sin 60^\circ=\frac{\sqrt{3}}{2}\approx 0.8660254038$$ $$a\approx 18\cdot\frac{0.9396926208}{0.8660254038}\approx 19.5319683$$ 4. Round to two decimal places to obtain the final answer. $$a\approx 19.53$$