1. **State the problem:** We need to find the area swept by the policeman's arm, which moves through an angle of 75° with a length (radius) of 60 cm. 2. **Understand the geometry:** The arm movement forms a sector of a circle with radius $r = 60$ cm and central angle $\theta = 75^\circ$. 3. **Formula for sector area:** The area $A$ of a sector with radius $r$ and angle $\theta$ (in degrees) is given by $$ A = \frac{\theta}{360} \times \pi r^2 $$ 4. **Substitute values:** $$ A = \frac{75}{360} \times \pi \times (60)^2 $$ 5. **Calculate inside the formula:** $$ A = \frac{75}{360} \times \pi \times 3600 $$ 6. **Simplify the fraction:** $$ \frac{75}{360} = \frac{5}{24} $$ 7. **Calculate the area:** $$ A = \frac{5}{24} \times \pi \times 3600 = 5 \times 150 \pi = 750 \pi $$ 8. **Final answer:** The area swept by the arm is $$ \boxed{750\pi\text{ cm}^2} $$