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. 100 km
B. 24 km
C. 55 km
D. 50 km

Explanation

To solve the problem of determining the distance over which signals from a TV transmission tower can be received via line of sight communication, we can use the following formula:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Height of the tower (h) = 240 m
- Radius of the Earth (r) = 6.4 × 10^6 m

2. **Use the Formula for Line of Sight Distance:**
The formula to calculate the distance (d) for line of sight communication is given by:
\[ d = \sqrt{2 \cdot r \cdot h} \]

3. **Substitute the Values into the Formula:**
We substitute the radius and height into the formula:
\[ d = \sqrt{2 \cdot (6.4 \times 10^6) \cdot (240)} \]

4. **Calculate the Value Inside the Square Root:**
First, calculate \(2 \cdot 6.4 \times 10^6 \cdot 240\):
\[ 2 \cdot 6.4 \times 10^6 = 12.8 \times 10^6 \]
\[ 12.8 \times 10^6 \cdot 240 = 3.072 \times 10^9 \]

5. **Take the Square Root:**
Now, we take the square root of \(3.072 \times 10^9\):
\[ d = \sqrt{3.072 \times 10^9} \approx 55.5 \times 10^3 \text{ m} \]

6. **Convert the Distance to Kilometers:**
To convert meters to kilometers, we divide by 1000:
\[ d \approx 55.5 \text{ km} \]

7. **Round the Result:**
Rounding to the nearest whole number gives us approximately:
\[ d \approx 55 \text{ km} \]

### Conclusion:
The distance over which the signals broadcast from the tower will be received is approximately **55 km**.