1. The problem involves resolving forces into their components along the x and y axes using trigonometric functions. 2. The formula for resolving a force $F$ at an angle $\theta$ into components is: - $F_x = F \cos \theta$ - $F_y = F \sin \theta$ 3. Important rules: - Angles are measured from the positive x-axis. - Cosine gives the adjacent side (x-component), sine gives the opposite side (y-component). 4. Calculate each component: - For $15N$ at $60^\circ$: $15 \cos 60^\circ = 15 \times 0.5 = 7.5$ $15 \sin 60^\circ = 15 \times 0.866 = 12.99$ - For $10N$ at $30^\circ$: $10 \cos 30^\circ = 10 \times 0.866 = 8.66$ $10 \sin 30^\circ = 10 \times 0.5 = 5$ - For $12.5N$ at $45^\circ$: $12.5 \cos 45^\circ = 12.5 \times 0.707 = 8.84$ $12.5 \sin 45^\circ = 12.5 \times 0.707 = 8.84$ - For $5N$ at $60^\circ$: $5 \cos 60^\circ = 5 \times 0.5 = 2.5$ $5 \sin 60^\circ = 5 \times 0.866 = 4.33$ 5. These components represent the forces along the x and y axes respectively. Final answers: - $15 \cos 60^\circ = 7.5$ - $15 \sin 60^\circ = 12.99$ - $10 \cos 30^\circ = 8.66$ - $10 \sin 30^\circ = 5$ - $12.5 \cos 45^\circ = 8.84$ - $12.5 \sin 45^\circ = 8.84$ - $5 \cos 60^\circ = 2.5$ - $5 \sin 60^\circ = 4.33$