At a particular station, the TV transmission tower has a height of $$100 \text{ m}$$. To triple its coverage range, height of the tower should be increased to

We are given that the TV transmission tower has a height of $$h = 100 \text{ m}$$ and we need to find the new height to triple its coverage range.

The coverage range (or line-of-sight distance) of a TV tower is given by:

$$d = \sqrt{2Rh}$$

where $$R$$ is the radius of the Earth and $$h$$ is the height of the tower.

Let the original range be $$d_1 = \sqrt{2R \times 100}$$ and the new range be $$d_2 = 3d_1$$.

For the new height $$h'$$:

$$d_2 = \sqrt{2Rh'}$$

Since $$d_2 = 3d_1$$:

$$\sqrt{2Rh'} = 3\sqrt{2R \times 100}$$

Squaring both sides:

$$2Rh' = 9 \times 2R \times 100$$

$$h' = 9 \times 100 = 900 \text{ m}$$

The correct answer is Option D: $$900 \text{ m}$$.