Question: PERFORMANCE TASK NO. 1 I. OBJECTIVES a. Solve word problems involving Sine law. b. Solve word problems involving Cosine law. II. MATERIALS NEEDED a. Worksheet # 1 b. Calculator c. Short Bondpapers d. Pen and Art Materials III. INSTRUCTIONS Copy the problems on a short bond paper. Read each problem carefully, analyze the given information, and solve it. Present all necessary diagrams, illustrations, and complete solutions CLEARLY AND NEATLY. 1. A fisherman wants to culture a pond of milkfish for their source of living. The pond is triangular. The longest side is 35 feet, while the measures of the two angles are 40° and 55°. Find the lengths of the other remaining sides so that he can put the right amount of net fence in his pond.

1. **Problem:** A fisherman has a triangular pond with the longest side measuring $35$ feet and two angles measuring $40^\circ$ and $55^\circ$. Find the lengths of the other two sides. 2. **Formula:** Use the Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a,b,c$ are sides opposite angles $A,B,C$ respectively. 3. **Step 1:** Find the third angle: $$C = 180^\circ - 40^\circ - 55^\circ = 85^\circ$$ 4. **Step 2:** Identify the longest side $c = 35$ feet opposite the largest angle $C = 85^\circ$. 5. **Step 3:** Use Law of Sines to find side $a$ opposite $A=40^\circ$: $$\frac{a}{\sin 40^\circ} = \frac{35}{\sin 85^\circ}$$ 6. **Step 4:** Solve for $a$: $$a = \frac{35 \times \sin 40^\circ}{\sin 85^\circ}$$ Calculate: $$a \approx \frac{35 \times 0.6428}{0.9962} \approx 22.58 \text{ feet}$$ 7. **Step 5:** Use Law of Sines to find side $b$ opposite $B=55^\circ$: $$\frac{b}{\sin 55^\circ} = \frac{35}{\sin 85^\circ}$$ 8. **Step 6:** Solve for $b$: $$b = \frac{35 \times \sin 55^\circ}{\sin 85^\circ}$$ Calculate: $$b \approx \frac{35 \times 0.8192}{0.9962} \approx 28.77 \text{ feet}$$ **Final answer:** The other two sides are approximately $22.58$ feet and $28.77$ feet.