1. **Problem Statement:** Find the resultant of two forces: 3N acting at 10 degrees and 5N acting at 120 degrees. 2. **Formula Used:** The resultant $R$ of two forces $F_1$ and $F_2$ acting at an angle $\theta$ between them is given by the law of cosines: $$R = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos(\theta)}$$ 3. **Step 1: Identify values** - $F_1 = 3$ - $F_2 = 5$ - Angle between forces $\theta = 120^\circ - 10^\circ = 110^\circ$ 4. **Step 2: Calculate $\cos(110^\circ)$** $$\cos(110^\circ) = \cos(180^\circ - 70^\circ) = -\cos(70^\circ) \approx -0.3420$$ 5. **Step 3: Substitute values into formula** $$R = \sqrt{3^2 + 5^2 + 2 \times 3 \times 5 \times (-0.3420)}$$ $$R = \sqrt{9 + 25 - 10.26} = \sqrt{23.74}$$ 6. **Step 4: Calculate resultant magnitude** $$R \approx 4.87$$ 7. **Interpretation:** The resultant force has a magnitude of approximately 4.87N.