1. The problem is to find the length of the side opposite to a given angle in a triangle. 2. The most common formula used is from the sine rule: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are the sides opposite angles $A$, $B$, and $C$ respectively. 3. To find the opposite side $a$ when you know angle $A$ and another side-angle pair, rearrange the formula: $$a = b \times \frac{\sin A}{\sin B}$$ 4. Another way is using the basic trigonometric definition in a right triangle: $$\sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}}$$ so the opposite side = hypotenuse $\times \sin \theta$. 5. Remember, the sine rule works for any triangle, while the trigonometric definition applies only to right triangles. 6. Example: If angle $A=30^\circ$ and side $b=10$ opposite angle $B=45^\circ$, then $$a = 10 \times \frac{\sin 30^\circ}{\sin 45^\circ} = 10 \times \frac{0.5}{0.7071} \approx 7.07$$. 7. This gives the length of the side opposite angle $A$.