A TV transmission tower has a height of 240 m. Signals broadcast from this tower will be received by LOS communication at a distance of (assume the radius of earth to be `6.4 xx 10 ^(6) m`)

Options

A. 100km
B. 110km
C. 55km
D. 120km

Explanation

To find the maximum distance at which signals broadcast from a TV transmission tower can be received using Line of Sight (LOS) communication, we can use the formula:

\[ d_{max} = \sqrt{2 h_t r_e} \]

Where:
- \( d_{max} \) is the maximum distance,
- \( h_t \) is the height of the transmission tower,
- \( r_e \) is the radius of the Earth.

### Step-by-Step Solution:

1. **Identify the given values**:
- Height of the transmission tower, \( h_t = 240 \) m
- Radius of the Earth, \( r_e = 6.4 \times 10^6 \) m

2. **Substitute the values into the formula**:
\[ d_{max} = \sqrt{2 \times h_t \times r_e} \]
\[ d_{max} = \sqrt{2 \times 240 \times (6.4 \times 10^6)} \]

3. **Calculate \( 2 \times 240 \)**:
\[ 2 \times 240 = 480 \]

4. **Multiply by the radius of the Earth**:
\[ 480 \times (6.4 \times 10^6) = 3.072 \times 10^9 \]

5. **Take the square root**:
\[ d_{max} = \sqrt{3.072 \times 10^9} \]
\[ d_{max} \approx 55,500 \text{ m} \quad \text{(after calculating the square root)} \]

6. **Convert to kilometers**:
\[ d_{max} \approx 55.5 \text{ km} \]

### Final Answer:
The maximum distance at which signals broadcast from the tower can be received is approximately **55.5 km**.