1. Let's state the problem: You want to find the length of a side in a triangle given only an angle, but no other information. 2. Important note: To find the length of a side in a triangle, you need at least one side length or some other measurement besides just an angle. This is because angles alone do not determine side lengths; triangles with the same angles can have different sizes (they are similar but not congruent). 3. The key formulas involving sides and angles in triangles are the Law of Sines and the Law of Cosines: - Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ - Law of Cosines: $$c^2 = a^2 + b^2 - 2ab\cos C$$ 4. Both laws require at least one known side length to find unknown sides. 5. Therefore, with only an angle and no side lengths or other information, it is impossible to find the length of a side uniquely. 6. If you get additional information such as one side length or another angle, you can then apply these laws to find the unknown side length.