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 maximum distance for Line of Sight (LOS) communication from a TV transmission tower of height 240 m, we can use the formula for the distance \( D \) that can be covered by LOS communication:

\[ D = \sqrt{2 \cdot R \cdot H} \]

Where:
- \( D \) is the distance in meters,
- \( R \) is the radius of the Earth (given as \( 6.4 \times 10^6 \) m),
- \( H \) is the height of the tower (given as 240 m).

### Step 1: Substitute the values into the formula
We start by substituting the values of \( R \) and \( H \) into the formula:

\[ D = \sqrt{2 \cdot (6.4 \times 10^6) \cdot 240} \]

### Step 2: Calculate the product inside the square root
Now, we calculate the product:

\[ 2 \cdot (6.4 \times 10^6) \cdot 240 \]

Calculating \( 2 \cdot 6.4 = 12.8 \), then:

\[ 12.8 \cdot 240 = 3072 \]

Thus, we have:

\[ D = \sqrt{3072 \times 10^6} \]

### Step 3: Calculate the square root
Now we calculate the square root:

\[ D = \sqrt{3072} \times 10^3 \]

Calculating \( \sqrt{3072} \):

\[ \sqrt{3072} \approx 55.4 \]

Thus, we have:

\[ D \approx 55.4 \times 10^3 \text{ m} \]

### Step 4: Convert meters to kilometers
To convert meters to kilometers, we divide by 1000:

\[ D \approx 55.4 \text{ km} \]

### Conclusion
The maximum distance for LOS communication from the TV transmission tower is approximately 55.4 km. Therefore, the correct option is 55 km.

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