1. **State the problem:** We need to find the size of a receiving antenna for a radio broadcast service operating at 120 MHz, given that the antenna size is about half the signal wavelength. 2. **Relevant formula:** The wavelength $\lambda$ of a signal is related to its frequency $f$ by the formula: $$\lambda = \frac{c}{f}$$ where $c$ is the speed of light, approximately $3 \times 10^8$ meters per second. 3. **Calculate the wavelength:** Given $f = 120$ MHz = $120 \times 10^6$ Hz, $$\lambda = \frac{3 \times 10^8}{120 \times 10^6} = \frac{3 \times 10^8}{1.2 \times 10^8} = 2.5 \text{ meters}$$ 4. **Calculate antenna size:** The antenna size is about half the wavelength, $$\text{Antenna size} = \frac{\lambda}{2} = \frac{2.5}{2} = 1.25 \text{ meters}$$ **Final answer:** The size of the receiving antenna should be approximately $1.25$ meters.