1. **Problem 1:** Given $m\angle B = 14^\circ$, side $a = 30$ yd, and side $b = 12$ yd, solve the triangle. 2. **Formula:** Use the Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 3. **Step 1:** Find angle $A$ using Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} \Rightarrow \sin A = \frac{a \sin B}{b} = \frac{30 \sin 14^\circ}{12}$$ Calculate $\sin 14^\circ \approx 0.2419$: $$\sin A = \frac{30 \times 0.2419}{12} = \frac{7.257}{12} = 0.6048$$ 4. **Step 2:** Find $A$: $$A = \sin^{-1}(0.6048) \approx 37.3^\circ$$ 5. **Step 3:** Find angle $C$: $$C = 180^\circ - A - B = 180^\circ - 37.3^\circ - 14^\circ = 128.7^\circ$$ 6. **Step 4:** Find side $c$ using Law of Sines: $$\frac{c}{\sin C} = \frac{a}{\sin A} \Rightarrow c = \frac{a \sin C}{\sin A} = \frac{30 \sin 128.7^\circ}{\sin 37.3^\circ}$$ Calculate $\sin 128.7^\circ \approx 0.7818$ and $\sin 37.3^\circ \approx 0.6048$: $$c = \frac{30 \times 0.7818}{0.6048} = \frac{23.454}{0.6048} \approx 38.8 \text{ yd}$$ **Final answers for Problem 1:** $$m\angle A \approx 37.3^\circ, \quad m\angle C \approx 128.7^\circ, \quad c \approx 38.8 \text{ yd}$$